Showing papers in "Computers & Mathematics With Applications in 2012"
TL;DR: The existence and uniqueness of global solutions in the space of weighted continuous functions are proved and the stability of the solution for a weighted Cauchy-type problem is analyzed.
Abstract: We consider an initial value problem for a class of nonlinear fractional differential equations involving Hilfer fractional derivative. We prove existence and uniqueness of global solutions in the space of weighted continuous functions. The stability of the solution for a weighted Cauchy-type problem is also analyzed.
348 citations
TL;DR: Four multi-objective optimization techniques are analyzed by describing their formulation, advantages and disadvantages and the effectiveness of the selected techniques for engineering design purposes is verified by comparing the results obtained by solving a few benchmarks and a real structural engineering problem concerning an engine bracket of a car.
Abstract: Computational models describing the behavior of complex physical systems are often used in the engineering design field to identify better or optimal solutions with respect to previously defined performance criteria. Multi-objective optimization problems arise and the set of optimal compromise solutions (Pareto front) has to be identified by an effective and complete search procedure in order to let the decision maker, the designer, to carry out the best choice. Four multi-objective optimization techniques are analyzed by describing their formulation, advantages and disadvantages. The effectiveness of the selected techniques for engineering design purposes is verified by comparing the results obtained by solving a few benchmarks and a real structural engineering problem concerning an engine bracket of a car.
302 citations
TL;DR: The concept of piecewise continuous solutions for impulsive Cauchy problems and impulsive boundary value problems respectively are introduced by using a new fixed point theorem and many new existence, uniqueness and data dependence results of solutions are obtained via some generalized singular Gronwall inequalities.
Abstract: In this paper, the first purpose is treating Cauchy problems and boundary value problems for nonlinear impulsive differential equations with Caputo fractional derivative. We introduce the concept of piecewise continuous solutions for impulsive Cauchy problems and impulsive boundary value problems respectively. By using a new fixed point theorem, we obtain many new existence, uniqueness and data dependence results of solutions via some generalized singular Gronwall inequalities. The second purpose is discussing Ulam stability for impulsive fractional differential equations. Some new concepts in stability of impulsive fractional differential equations are offered from different perspectives. Some applications of our results are also provided.
213 citations
TL;DR: A new identity similar to an identity proved in Alomari et al. (2010) for fractional integrals is established and some new Ostrowski type inequalities for Riemann-Liouville fractional integral are established by making use of the established identity.
Abstract: A new identity similar to an identity proved in Alomari et al. (2010) [15] for fractional integrals is established. Then by making use of the established identity, some new Ostrowski type inequalities for Riemann-Liouville fractional integral are established. Our results have some relationships with the results of Alomari et al. (2010), proved in [15] and the analysis used in the proofs is simple.
194 citations
TL;DR: Experimental data demonstrate that the WSN topology obtained has the property of weighted networks of the IOT: the edge weight, vertex degree, and strength follow a power-law distribution.
Abstract: In this paper, we propose a new constructing approach for a weighted topology of wireless sensor networks (WSNs) based on local-world theory for the Internet of Things (IOT). Based on local-world theory, an uneven clustering weighted evolving model of WSNs is designed. The definitions of edge weight and vertex strength take sensor energy, transmission distance, and flow into consideration. The vertex strengths drive the growth of topology; meanwhile, the edge weights change correspondingly. Experimental data demonstrate that the WSN topology we obtain has the property of weighted networks of the IOT: the edge weight, vertex degree, and strength follow a power-law distribution. Related IOT research work shows that weighted WSNs not only share the robustness and fault tolerance of weight-free networks, but also reduce the probability that successive node breakdowns occur; furthermore, they enhance the synchronization of WSNs.
192 citations
TL;DR: This paper proposes computationally effective implicit numerical methods for fractional advection-dispersion models that can be used to simulate the regional-scale anomalous dispersion with heavy tails.
Abstract: In this paper, a class of fractional advection-dispersion models (FADMs) is considered. These models include five fractional advection-dispersion models, i.e., the time FADM, the mobile/immobile time FADM with a time Caputo fractional derivative 0<@c<1, the space FADM with two sides Riemann-Liouville derivatives, the time-space FADM and the time fractional advection-diffusion-wave model with damping with index 1<@c<2. These equations can be used to simulate the regional-scale anomalous dispersion with heavy tails. We propose computationally effective implicit numerical methods for these FADMs. The stability and convergence of the implicit numerical methods are analysed and compared systematically. Finally, some results are given to demonstrate the effectiveness of theoretical analysis.
189 citations
TL;DR: A detailed procedure solves complex GSCM strategy-selection problems and evaluates the most important activity in each business function, and proposes a network to clarify managerial levels and firm-related content.
Abstract: This study designates green supply chain management (GSCM) strategies to effectively direct business functions and activities in the electronics industry. Enterprises conduct environmental scanning to understand the external environment and internal functions; a successful strategy identifies unique firm-owned resources and transforms them into capabilities. This study proposes a network to clarify managerial levels and firm-related content. It derives four business functions from product lifecycle management: design, purchasing, manufacturing, and marketing and service-and associates their related activities with ''greenness''. These functions and activities are a network's clusters and elements in an analytic network process (ANP) model with dependent relations. A detailed procedure solves complex GSCM strategy-selection problems and evaluates the most important activity in each business function. A case study takes a leading Taiwanese electronics company to identify the proposed procedure's stability.
177 citations
TL;DR: Coupled coincidence and common coupled fixed point theorems for (@j,@f)-weakly contractive mappings in ordered G-metric spaces are established.
Abstract: In this paper, we establish coupled coincidence and common coupled fixed point theorems for (@j,@f)-weakly contractive mappings in ordered G-metric spaces. Presented theorems extend, generalize and improve many existing results in the literature. An example is given.
150 citations
TL;DR: A new set of sufficient conditions for approximate controllability of fractional stochastic differential equations is formulated and proved and the compactness of semigroup is not assumed and subsequently the conditions are obtained for exact controllable result.
Abstract: A class of dynamic control systems described by nonlinear fractional stochastic differential equations in Hilbert spaces is considered. Using fixed point technique, fractional calculations, stochastic analysis technique and methods adopted directly from deterministic control problems, a new set of sufficient conditions for approximate controllability of fractional stochastic differential equations is formulated and proved. In particular, we discuss the approximate controllability of nonlinear fractional stochastic control system under the assumptions that the corresponding linear system is approximately controllable. The results in this paper are generalization and continuation of the recent results on this issue. An example is provided to show the application of our result. Finally as a remark, the compactness of semigroup is not assumed and subsequently the conditions are obtained for exact controllability result.
148 citations
TL;DR: The systems being considered are a special instance of real-time cyber-physical-human systems that have become a crucial component of all large scale physical infrastructures such as buildings, campuses, sports and entertainment venues, and transportation hubs.
Abstract: This paper surveys recent research on the use of sensor networks, communications and computer systems to enhance the human outcome of emergency situations. Areas covered include sensing, communication with evacuees and emergency personnel, path finding algorithms for safe evacuation, simulation and prediction, and decision tools. The systems being considered are a special instance of real-time cyber-physical-human systems that have become a crucial component of all large scale physical infrastructures such as buildings, campuses, sports and entertainment venues, and transportation hubs.
146 citations
TL;DR: It is demonstrated that revised equations, including the initial state vector of the fractional integrator provide corrected free responses which match with real transients, as exhibited by numerical simulations.
Abstract: Fractional order differentiation is generally considered as the basis of fractional calculus, but the real basis is in fact fractional order integration and particularly the fractional integrator, because definition and properties of fractional differentiation and of fractional differential systems rely essentially on fractional integration. We present the frequency distributed model of the fractional integrator and its finite dimension approximation. The simulation of FDSs, based on fractional integrators, leads to the definition of FDS internal state variables, which are the state variables of the fractional integrators, as a generalization of the integer order case. The initial condition problem has been an open problem for a long time in fractional calculus. We demonstrate that the frequency distributed model of the fractional integrator provides a solution to this problem through the knowledge of its internal state. Beyond the solution of this fundamental problem, mastery of the integrator internal state allows the analysis and prediction of fractional differential system transients. Moreover, the finite dimension approximation of the fractional integrator provides an efficient technique for practical simulation of FDSs and analysis of their transients, with a particular insight into the interpretation of initial conditions, as illustrated by numerical simulations. Laplace transform equations and initial conditions of the Caputo and the Riemann-Liouville derivatives are used to formulate the free responses of FDEs. Because usual equations are wrong, the corresponding free responses do not fit with real transients. We demonstrate that revised equations, including the initial state vector of the fractional integrator (used to perform differentiation) provide corrected free responses which match with real transients, as exhibited by numerical simulations.
TL;DR: By means of a fixed point theorem, the existence and multiplicity of positive solutions for the singular fractional boundary value problem are obtained.
Abstract: In this paper, we discuss the existence and multiplicity of positive solutions for the singular fractional boundary value problem D 0 + α u ( t ) + f ( t , u ( t ) , D 0 + ν u ( t ) , D 0 + μ u ( t ) ) = 0 , u ( 0 ) = u ′ ( 0 ) = u ″ ( 0 ) = u ″ ( 1 ) = 0 , where 3 α ≤ 4 , 0 ν ≤ 1 , 1 μ ≤ 2 , D 0 + α is the standard Riemann–Liouville fractional derivative, f is a Carathedory function and f ( t , x , y , z ) is singular at the value 0 of its arguments x , y , z . By means of a fixed point theorem, the existence and multiplicity of positive solutions are obtained.
TL;DR: It is proved that the sequences generated by the proposed algorithm converge weakly to an element of Fix(S)@[email protected] under mild conditions.
Abstract: The purpose of this paper is to introduce and analyze an extragradient method with regularization for finding a common element of the solution set @C of the split feasibility problem and the set Fix(S) of fixed points of a nonexpansive mapping S in the setting of infinite-dimensional Hilbert spaces. Combining the regularization method and the extragradient method due to Nadezhkina and Takahashi [N. Nadezhkina, W. Takahashi, Weak convergence theorem by an extragradient method for nonexpansive mappings and monotone mappings, J. Optim. Theory Appl. 128 (2006) 191-201], we propose an iterative algorithm for finding an element of Fix(S)@[email protected] We prove that the sequences generated by the proposed algorithm converge weakly to an element of Fix(S)@[email protected] under mild conditions.
TL;DR: The fixed point theorem combined with solutions operator theorems results show the existence of mild solutions for fractional differential equations with nonlocal conditions of order 1<@a<2.
Abstract: This paper is mainly concerned with the existence of mild solutions for fractional differential equations with nonlocal conditions of order 1<@a<2. The results are obtained by the fixed point theorem combined with solutions operator theorems.
TL;DR: A general framework to find the solutions for impulsive fractional boundary value problems, which will provide an effective way to deal with such problems.
Abstract: This paper is motivated from some recent papers treating the boundary value problems for impulsive fractional differential equations. We first make a counterexample to show that the formula of solutions in cited papers are incorrect. Second, we establish a general framework to find the solutions for impulsive fractional boundary value problems, which will provide an effective way to deal with such problems. Third, some sufficient conditions for the existence of the solutions are established by applying fixed point methods. Meanwhile, data dependence is obtained by using a new generalized singular Gronwall inequality. Finally, three examples are given to illustrate the results.
TL;DR: In this article, a method of separating variables is used to solve the multi-term time-fractional diffusion-wave equation and the multiscale time fractional diffusion equation in a finite domain.
Abstract: Multi-term time-fractional differential equations have been used for describing important physical phenomena. However, studies of the multi-term time-fractional partial differential equations with three kinds of nonhomogeneous boundary conditions are still limited. In this paper, a method of separating variables is used to solve the multi-term time-fractional diffusion-wave equation and the multi-term time-fractional diffusion equation in a finite domain. In the two equations, the time-fractional derivative is defined in the Caputo sense. We discuss and derive the analytical solutions of the two equations with three kinds of nonhomogeneous boundary conditions, namely, Dirichlet, Neumann and Robin conditions, respectively.
TL;DR: In this paper, the authors carried out extensive global optimization of unconstrained and constrained problems using the recently developed eagle strategy by Yang and Deb in combination with the efficient differential evolution.
Abstract: The performance of an optimization tool is largely determined by the efficiency of the search algorithm used in the process The fundamental nature of a search algorithm will essentially determine its search efficiency and thus the types of problems it can solve Modern metaheuristic algorithms are generally more suitable for global optimization This paper carries out extensive global optimization of unconstrained and constrained problems using the recently developed eagle strategy by Yang and Deb in combination with the efficient differential evolution After a detailed formulation and explanation of its implementation, the proposed algorithm is first verified using twenty unconstrained optimization problems or benchmarks For the validation against constrained problems, this algorithm is subsequently applied to thirteen classical benchmarks and three benchmark engineering problems reported in the engineering literature The performance of the proposed algorithm is further compared with various, state-of-the-art algorithms in the area The optimal solutions obtained in this study are better than the best solutions obtained by the existing methods The unique search features used in the proposed algorithm are analyzed, and their implications for future research are also discussed in detail
TL;DR: A potato defect detection combining with size sorting system using the machine vision will be proposed, and the mathematics methods used in automation with a particular emphasis on the issues associated with designing, implementing and using classification algorithms to solve equations.
Abstract: Detection of external defects on potatoes is the most important technology in the realization of automatic potato sorting stations. This paper presents a hierarchical grading method applied to the potatoes. In this work a potato defect detection combining with size sorting system using the machine vision will be proposed. This work also will focus on the mathematics methods used in automation with a particular emphasis on the issues associated with designing, implementing and using classification algorithms to solve equations. In the first step, a simple size sorting based on mathematical binarization is described, and the second step is to segment the defects; to do this, color based classifiers are used. All the detection standards for this work are referenced from the United States Agriculture Department, and Canadian Food Industries. Results show that we have a high accuracy in both size sorting and classification. Experimental results show that support vector machines have very high accuracy and speed between classifiers for defect detection.
TL;DR: Some common fixed pointTheorems satisfying certain rational expressions are proved in complex valued metric spaces which generalize fixed point theorems due to Azam et al., Imdad et al. and others.
Abstract: Some common fixed point theorems satisfying certain rational expressions are proved in complex valued metric spaces which generalize fixed point theorems due to Azam et al., Imdad et al. and others. Some related results are also derived besides furnishing illustrative examples to highlight the realized improvements.
TL;DR: The circuit model, fractional-order state equations and the numerical technique are introduced and various examples are introduced with different fractional orders using the non-standard finite difference scheme together with the Grunwald-Letnikov discretization process which is easily implemented and reliably accurate.
Abstract: In this paper, we generalize the integer-order cable model of the neuron system into the fractional-order domain, where the long memory dependence of the fractional derivative can be a better fit for the neuron response. Furthermore, the chaotic synchronization with a gap junction of two or multi-coupled-neurons of fractional-order are discussed. The circuit model, fractional-order state equations and the numerical technique are introduced in this paper for individual and multiple coupled neuron systems with different fractional-orders. Various examples are introduced with different fractional orders using the non-standard finite difference scheme together with the Grunwald-Letnikov discretization process which is easily implemented and reliably accurate.
TL;DR: The main results are that the classification of each attribute into absolutely necessary, relatively necessary and absolutely unnecessary attributes is independent of the framework considered and that an attribute reduction in one of these relational systems is also an attribute reduct in the others.
Abstract: Attribute reduction is an important step in reducing computational complexity in order to extract information from relational systems. Three of these systems are the formal, object-oriented and property oriented concept lattices. Attribute reduction in the last two concept lattices has recently been studied. The relation with the first concept lattice is very important since two important, independent tools to extract information from databases-the formal concept analysis and rough set theory-will be related. This paper studies attribute reduction in these three frameworks. The main results are that the classification of each attribute into absolutely necessary, relatively necessary and absolutely unnecessary attributes is independent of the framework considered and that an attribute reduct in one of these relational systems is also an attribute reduct in the others.
TL;DR: Nonlinear hysteresis modeling is studied using a novel PZT-actuated flexure-based mechanism and the capability of the proposed controller to achieve precision tracking tasks with submicron precision is validated.
Abstract: Nonlinear hysteresis modeling is studied using a novel PZT-actuated flexure-based mechanism. To compare the performance of variant hysteresis models with respect to the tracking reference, we reformulate the Bouc-Wen model, the Dahl model and the Duhem model as a generalized Duhem model. System parameters for these three hysteresis models are formulated into nonlinear optimization problems with constraints. These optimization problems are solved by the particle swarm optimization method. Since the Duhem model includes both electrical and mechanical domains, it has a smaller modeling error compared to the other two hysteresis models. The simulation results are confirmed by modeling the proposed biaxial piezo-actuated positioning stage of these hysteresis models. Cross-coupling effects between the X- and Y-axis actuation are also alleviated by a novel feedforward compensation mechanism based on the Duhem model with crossover terms. Finally, a real-time experiment is performed to confirm the feasibility of the proposed method. The experimental results validate the capability of the proposed controller to achieve precision tracking tasks with submicron precision.
TL;DR: A new chaotic firefly algorithm approach based on Tinkerbell map (CFA) to tune multi-loop PID multivariable controllers and results indicate that a suitable set of PID parameters can be calculated by the proposed CFA.
Abstract: Nowadays, a variety of controllers used in process industries are still of the proportional-integral-derivative (PID) types. PID controllers have the advantage of simple structure, good stability, and high reliability. A relevant issue for PID controllers design is the accurate and efficient tuning of parameters. In this context, several approaches have been reported in the literature for tuning the parameters of PID controllers using evolutionary algorithms, mainly for single-input single-output systems. The systematic design of multi-loop (or decentralized) PID control for multivariable processes to meet certain objectives simultaneously is still a challenging task. This paper proposes a new chaotic firefly algorithm approach based on Tinkerbell map (CFA) to tune multi-loop PID multivariable controllers. The firefly algorithm is a metaheuristic algorithm based on the idealized behavior of the flashing characteristics of fireflies. To validate the performance of the proposed PID control design, a multi-loop multivariable PID structure for a binary distillation column plant (Wood and Berry column model) and an industrial-scale polymerization reactor are taken. Simulation results indicate that a suitable set of PID parameters can be calculated by the proposed CFA. Besides, some comparison results of a genetic algorithm, a particle swarm optimization approach, traditional firefly algorithm, modified firefly algorithm, and the proposed CFA to tune multi-loop PID controllers are presented and discussed.
TL;DR: A multivariable control strategy for the waste heat recovery system is proposed by incorporating a linear quadratic regulator (LQR) with a PI controller, and simulations demonstrate that the proposed strategy can obtain satisfactory performance.
Abstract: In this paper, the dynamics of organic Rankine cycles (ORCs) in waste heat utilizing processes is investigated, and the physical model of a 100 kW waste heat utilizing process is established. In order to achieve both transient performance and steady-state energy saving, a multivariable control strategy for the waste heat recovery system is proposed by incorporating a linear quadratic regulator (LQR) with a PI controller. Simulations demonstrate that the proposed strategy can obtain satisfactory performance.
TL;DR: The steady mixed convection boundary layer flow of an incompressible nanofluid along a plate inclined at an angle @a in a porous medium is studied and the Nusselt number is found to decrease with increasing Brownian motion number (Nb) or thermophoresis number (nt), whereas it increases with increasing angle @ a.
Abstract: The steady mixed convection boundary layer flow of an incompressible nanofluid along a plate inclined at an angle @a in a porous medium is studied. The resulting nonlinear governing equations with associated boundary conditions are solved using an optimized, robust, extensively validated, variational finite-element method (FEM) and a finite-difference method (FDM) with a local non-similar transformation. The Nusselt number is found to decrease with increasing Brownian motion number (Nb) or thermophoresis number (Nt), whereas it increases with increasing angle @a. In addition, the local Sherwood number is found to increase with a rise in Nt, whereas it is reduced with an increase in Nb and angle @a. The effects of Lewis number, buoyancy ratio, and mixed convection parameter on temperature and concentration distributions are also examined in detail. The present study is of immediate interest in next-generation solar film collectors, heat-exchanger technology, material processing exploiting vertical and inclined surfaces, geothermal energy storage, and all those processes which are greatly affected by a heat-enhancement concept.
TL;DR: The authors derived several classes of soliton solutions in 2+1 dimensions and showed that the two-dimensional nonlinear Schrodinger equation is reduced either to the sine-Gordon for the hyperbolic case or sinh-Gordon equations for the elliptic case.
Abstract: In this paper, the authors extended the derivation to the nonlinear Schrodinger equation in two-dimensions, modified by the effect of non-uniformity. The authors derived several classes of soliton solutions in 2+1 dimensions. When the solution is assumed to depend on space and time only through a single argument of the function, they showed that the two-dimensional nonlinear Schrodinger equation is reduced either to the sine-Gordon for the hyperbolic case or sinh-Gordon equations for the elliptic case. Moreover, the authors extended this method to obtain analytical solutions to the nonlinear Schrodinger equation in two space dimensions plus time. This contains some interesting solutions such as the plane solitons, the N multiple solitons, the propagating breathers and quadratic solitons. The authors displayed graphically the obtained solutions by using the software Mathematica 5.
TL;DR: A novel mobile cloud execution framework is proposed to execute mobile applications in a cloud-based virtualized execution environment controlled by mobile applications and users, with encryption and isolation to protect against eavesdropping from cloud providers.
Abstract: Modern mobile devices, such as smartphones and tablets, have made many pervasive computing dreams come true. Still, many mobile applications do not perform well due to the shortage of resources for computation, data storage, network bandwidth, and battery capacity. While such applications can be re-designed with client-server models to benefit from cloud services, the users are no longer in full control of the application, which has become a serious concern for data security and privacy. In addition, the collaboration between a mobile device and a cloud server poses complex performance issues associated with the exchange of application state, synchronization of data, network condition, etc. In this work, a novel mobile cloud execution framework is proposed to execute mobile applications in a cloud-based virtualized execution environment controlled by mobile applications and users, with encryption and isolation to protect against eavesdropping from cloud providers. Under this framework, several efficient schemes have been developed to deal with technical issues for migrating applications and synchronizing data between execution environments. The communication issues are also addressed in the virtualization execution environment with probabilistic communication Quality-of-Service (QoS) technique to support timely application migration.
TL;DR: A threshold number @l@? of treated male mosquitoes is obtained above which the control of wild female mosquitoes is effective and the equilibrium 0 is GAS, with the trivial equilibrium 0 being globally asymptotically stable (GAS) when R@?1.
Abstract: The Sterile Insect Technology (SIT) is a nonpolluting method of control of the invading insects that transmit disease. The method relies on the release of sterile or treated males in order to reduce the wild population of anopheles mosquito. We propose two mathematical models. The first model governs the dynamics of the anopheles mosquito. The second model, the SIT model, deals with the interaction between treated males and wild female anopheles. Using the theory of monotone operators, we obtain dynamical properties of a global nature that can be summarized as follows. Both models are dissipative dynamical systems on the positive cone R"+^4. The value R=1 of the basic offspring number R is a forward bifurcation for the model of the anopheles mosquito, with the trivial equilibrium 0 being globally asymptotically stable (GAS) when R@?1, whereas 0 becomes unstable and one stable equilibrium is born with well determined basins of attraction when R>1. For the SIT model, we obtain a threshold number @l@? of treated male mosquitoes above which the control of wild female mosquitoes is effective. That is, for @l>@l@? the equilibrium 0 is GAS. When 0<@l@?@l@?, the number of equilibria and their stability are described together with their precise basins of attraction. These theoretical results are rephrased in terms of possible strategies for the control of the anopheles mosquito and they are illustrated by numerical simulations.
TL;DR: The authors' analysis rely on Banach fixed point theorem, nonlinear differentiation of Leray-Schauder type and the fixed point theorems of cone expansion and compression of norm type for positive solutions to a general class of integral boundary value problems for a coupled system of fractional differential equations.
Abstract: In the this paper, we establish sufficient conditions for the existence and nonexistence of positive solutions to a general class of integral boundary value problems for a coupled system of fractional differential equations. The differential operator is taken in the Riemann-Liouville sense. Our analysis rely on Banach fixed point theorem, nonlinear differentiation of Leray-Schauder type and the fixed point theorems of cone expansion and compression of norm type. As applications, some examples are also provided to illustrate our main results.
TL;DR: The univariate fractional quantitative approximation of real valued functions on a compact interval by quasi-interpolation sigmoidal and hyperbolic tangent neural network operators results into higher order converges better than the ordinary ones.
Abstract: Here, we study the univariate fractional quantitative approximation of real valued functions on a compact interval by quasi-interpolation sigmoidal and hyperbolic tangent neural network operators. These approximations are derived by establishing Jackson type inequalities involving the moduli of continuity of the right and left Caputo fractional derivatives of the engaged function. The approximations are pointwise and with respect to the uniform norm. The related feed-forward neural networks are with one hidden layer. Our fractional approximation results into higher order converges better than the ordinary ones.