Showing papers in "The Journal of Nonlinear Sciences and Applications in 2016"
TL;DR: In this paper, the power of the absolute of the first derivative is defined as a generalized (s,m)-preinvex function, and a Hadamard-Simpson type integral inequality is established for a function of which the power is generalized.
Abstract: The authors introduce the concepts of m-invex set, generalized (s,m)-preinvex function, and explicitly (s,m)-preinvex function, provide some properties for the newly introduced functions, and establish new Hadamard-Simpson type integral inequalities for a function of which the power of the absolute of the first derivative is generalized (s,m)-preinvex function. By taking different values of the parameters, Hadamardtype and Simpson-type integral inequalities can be deduced. Furthermore, inequalities obtained in special case present a refinement and improvement of previously known results. c ©2016 All rights reserved.
100 citations
TL;DR: In this paper, the authors presented the nonlinear Baggs and Freedman model with new fractional derivative and derived the special solution using an iterative method using the fixed point theory.
Abstract: We presented the nonlinear Baggs and Freedman model with new fractional derivative. We derived the special solution using an iterative method. The stability of the iterative method was presented using the fixed point theory. The uniqueness of the special solution was presented in detail using some properties of the inner product and the Hilbert space. We presented some numerical simulations to underpin the effectiveness of the used derivative and semi-analytical method. c ©2016 All rights reserved.
96 citations
TL;DR: Some inequalities of Hermite-Hadamard type for MT-convex functions via classical integrals and RiemannLiouville fractional integrals are introduced, respectively, and applications for special means are given as discussed by the authors.
Abstract: Some inequalities of Hermite-Hadamard type for MT-convex functions via classical integrals and RiemannLiouville fractional integrals are introduced, respectively, and applications for special means are given. Some error estimates for the trapezoidal formula are also obtained. c ©2016 All rights reserved.
93 citations
TL;DR: In this paper, the Hermite-Hadamard type inequalities for products of two convex and s-convex functions via Riemann-Liouville integrals are also established.
Abstract: In this paper, we establish some new Hermite-Hadamard inequalities for s-convex functions via fractional integrals. Some Hermite-Hadamard type inequalities for products of two convex and s-convex functions via Riemann-Liouville integrals are also established. c ©2016 All rights reserved.
75 citations
TL;DR: In this article, two novel integral identities for twice differentiable functions were discovered for classical integrals and Riemann-Liouville fractional integrals via functions whose derivatives absolute values are MTconvex.
Abstract: In this paper, we discover two novel integral identities for twice differentiable functions. Under the utility of these identities, we establish some generalized inequalities for classical integrals and Riemann-Liouville fractional integrals of the Hermite-Hadamard type via functions whose derivatives absolute values are MTconvex. At the end, we present applications for special means and several error approximations for the trapezoidal formula. c ©2016 All rights reserved.
72 citations
TL;DR: In this paper, the concept of well-posedness was generalized to a system of hemivariational inequalities in Banach space, and the equivalence results of strong (generalized) wellposedness between such a system and its derived system of inclusion problems were established.
Abstract: In this paper, we generalize the concept of well-posedness to a system of hemivariational inequalities in Banach space. By introducing several concepts of well-posedness for systems of hemivariational inequalities considered, we establish some metric characterizations of well-posedness and prove some equivalence results of strong (generalized) well-posedness between a system of hemivariational inequalities and its derived system of inclusion problems. c ©2016 All rights reserved.
61 citations
53 citations
TL;DR: In this paper, the authors studied a class of operator equations A(x, x) + B(x and x) = x in ordered Banach spaces, where A,B are two mixed monotone operators and associated theorems are established to guarantee the existence of a unique solution to the problem.
Abstract: In this paper we study a class of operator equations A(x, x) + B(x, x) = x in ordered Banach spaces, where A,B are two mixed monotone operators. Various theorems are established to guarantee the existence of a unique solution to the problem. In addition, associated iterative schemes have been established for finding the approximate solution converging to the fixed point of the problem. We also study the solution of the nonlinear eigenvalue equation A(x, x) + B(x, x) = λx and discuss its dependency to the parameter. Our results extend and improve many known results in this field of study. We have also successfully demonstrated the application of our results to the study of nonlinear fractional differential equations with two-point boundary conditions. c ©2016 All rights reserved.
51 citations
TL;DR: In this paper, the residual power series method (RPSM) is applied to find the exact solutions of fractional-order time dependent Schrödinger equations, and the competency of the method is examined by applying it to the several numerical examples.
Abstract: In this paper, the residual power series method (RPSM) is effectively applied to find the exact solutions of fractional-order time dependent Schrödinger equations. The competency of the method is examined by applying it to the several numerical examples. Mainly, we find that our solutions obtained by the proposed method are completely compatible with the solutions available in the literature. The obtained results interpret that the proposed method is very effective and simple for handling different types of fractional differential equations (FDEs). c ©2016 All rights reserved.
50 citations
TL;DR: For a higher-order nonlinear impulsive ordinary differential equation, the authors presented the concepts of Hyers-Ulam stability, generalized Hyers Ulam stability and generalized Ulam-Rassias stability for piecewise continuous functions.
Abstract: For a higher-order nonlinear impulsive ordinary differential equation, we present the concepts of Hyers– Ulam stability, generalized Hyers–Ulam stability, Hyers–Ulam–Rassias stability, and generalized Hyers– Ulam–Rassias stability. Furthermore, we prove the generalized Hyers–Ulam–Rassias stability by using integral inequality of Grönwall type for piecewise continuous functions. These results extend related contributions to the corresponding first-order impulsive ordinary differential equation. Hyers–Ulam stability, generalized Hyers–Ulam stability, and Hyers–Ulam–Rassias stability can be discussed by the same methods. c ©2016 All rights reserved.
48 citations
TL;DR: In this paper, two inverse problems for the wave equation with involution were considered and results on existence and uniqueness of solutions of these problems were presented, and they were shown to be the same as those in this paper.
Abstract: Two inverse problems for the wave equation with involution are considered. Results on existence and uniqueness of solutions of these problems are presented. c ©2016 All rights reserved.
TL;DR: In this article, Atangana and Baleanu proposed a derivative that is based upon the generalized Mittag-Leffler function, which is more suitable in expressing nature than power function.
Abstract: The power law has been used to construct the derivative with fractional order in Caputo and RiemannLiouville sense, if we viewed them as a convolution. However, it is not always possible to find the power law behaviour in nature. In 2016 Abdon Atangana and Dumitru Baleanu proposed a derivative that is based upon the generalized Mittag-Leffler function, since the Mittag-Leffler function is more suitable in expressing nature than power function. In this paper, we applied their new finding to the model of groundwater flowing within an unconfined aquifer. c ©2016 All rights reserved.
TL;DR: In this article, an extension of Caputo fractional derivative operator is introduced, and the extended fractional derivatives of some elementary functions are calculated, and linear and bilinear generating relations for extended hypergeometric functions are obtained.
Abstract: In this paper, an extension of Caputo fractional derivative operator is introduced, and the extended fractional derivatives of some elementary functions are calculated. At the same time, extensions of some hypergeometric functions and their integral representations are presented by using the extended fractional derivative operator, linear and bilinear generating relations for extended hypergeometric functions are obtained, and Mellin transforms of some extended fractional derivatives are also determined. c ©2016 All rights reserved.
TL;DR: In this article, the Hermite-Hadamard type inequalities involving fractional integrals with respect to another function were established, which generalize the Riemann-Liouville fractional integration and the Hadamard fractional integral integral.
Abstract: In this paper we establish new Hermite-Hadamard type inequalities involving fractional integrals with respect to another function. Such fractional integrals generalize the Riemann-Liouville fractional integrals and the Hadamard fractional integrals. c ©2016 All rights reserved.
TL;DR: In this paper, the authors introduce the concept of bipolar metric space as a type of partial distance and explore the link between metric spaces and bipolar metric spaces, especially in the context of completeness, and prove some extensions of known fixed point theorems.
Abstract: In this paper we introduce the concept of bipolar metric space as a type of partial distance. We explore the link between metric spaces and bipolar metric spaces, especially in the context of completeness, and prove some extensions of known fixed point theorems. c ©2016 All rights reserved.
TL;DR: In this paper, the existence and uniqueness of fixed point for a mapping in b-metric spaces is investigated and the wellposedness of the fixed point problem and the Ulam-Hyres stability is also studied.
Abstract: In this paper we introduce the notion of (α∗ − ψ)Ćirić-type contractive multivalued operator and investigate the existence and uniqueness of fixed point for such a mapping in b-metric spaces. The wellposedness of the fixed point problem and the Ulam-Hyres stability is also studied. c ©2016 All rights reserved.
TL;DR: In this paper, the locations of the collinear libration points in the restricted three-body problem are determined when the bigger primary is a triaxial rigid body and the analysis of the periodic motion around these points is performed and given up to second order in the case that the initial state of the motion gives rise to periodic orbits.
Abstract: The locations for the collinear libration points in the framework of the restricted three-body problem are determined when the bigger primary is a triaxial rigid body. The analysis of the periodic motion around these points is performed and given up to second order in the case that the initial state of the motion gives rise to periodic orbits. Moreover, some numerical results for the locations of collinear points are provided and the graphical investigations for the periodic motion are plotted, as well. It is worth mentioning that the collinear libration points and associated periodic orbits are considered the optimal placement to transfer a spacecraft to the nominal periodic orbits or to an associated stable manifold. c ©2016 All rights reserved.
TL;DR: In this paper, a generalization of the Banach fixed point theorem for image processing is presented. But this theorem is only applicable to digital images and cannot be applied to image processing.
Abstract: In this paper, we prove Banach fixed point theorem for digital images. We also give the proof of a theorem which is a generalization of the Banach contraction principle. Finally, we deal with an application of Banach fixed point theorem to image processing. c ©2015 All rights reserved.
TL;DR: In this article, the concept of modified F -contractions via α-admissible pair of mappings was introduced and several common fixed point results in the setting of metric spaces were provided.
Abstract: In this paper, we introduce the concept of modified F -contractions via α-admissible pair of mappings. We also provide several common fixed point results in the setting of metric spaces. Moreover, we present some illustrated examples and we give two applications on a dynamic programming and an integral equation. c ©2016 All rights reserved.
TL;DR: In this article, the nonlinear partial differential equations are reduced to nonlinear ordinary differential equations via similarity approach and further solved using shooting-RK4 method and validated with homotopy-Padé solutions.
Abstract: Heat absorption and thermal radiation effects in a non-Newtonian fluid on a vertical stretching sheet with suspended particles are considered. The nonlinear partial differential equations are reduced to nonlinear ordinary differential equations via similarity approach. The equations are further solved using shootingRK4 method and validated with homotopy-Padé solutions. Comparison between previous and present results revealed agreement up to five significant figures. The influence of various parameters on the flow velocity, temperature and concentration are examined. The profiles of reduced skin friction coefficient, Nusselt number and Sherwood number against selected parameters are sketched and discussed. Streamlines of the flow for different Maxwell parameters are visualized too. It is proclaimed that the heat flux of the flow is uplifted as value of either heat absorption or thermal radiation is multiplied. c ©2016 All rights reserved.
TL;DR: In this article, the authors construct some new non-linear differential equations and investigate the solutions of these nonlinear differential equation and give some new identities involving degenerate Euler numbers and polynomials arising from those nonlinear equations.
Abstract: The purpose of this paper is to construct some new non-linear differential equations and investigate the solutions of these non-linear differential equations. In addition, we give some new identities involving degenerate Euler numbers and polynomials arising from those non-linear differential equations. (C) 2016 All rights reserved.
TL;DR: In this article, the concept of α-admissible pairs of mappings was introduced and several common fixed point results in the setting of b-metric-like spaces were established.
Abstract: In this paper, using the concept of α-admissible pairs of mappings, we prove several common fixed point results in the setting of b-metric-like spaces. We also introduce the notion of generalized cyclic contraction pairs and establish some common fixed results for such pairs in b-metric-like spaces. Some examples are presented making effective the new concepts and results. Moreover, as consequences we prove some common fixed point results for generalized contraction pairs in partially ordered b-metric-like spaces. c ©2016 All rights reserved.
TL;DR: In this article, a new numerical approach, embedding the differential transform (DT) and Laplace transform (LT), is firstly proposed, which is considered in the local fractional derivative operator for obtaining the non-differential solution for diffusion equation in fractal heat transfer.
Abstract: In this paper, a new numerical approach, embedding the differential transform (DT) and Laplace transform (LT), is firstly proposed. It is considered in the local fractional derivative operator for obtaining the non-differential solution for diffusion equation in fractal heat transfer. c ©2016 All rights reserved.
TL;DR: In this article, a quasi-φ-none-expansive mapping and a generalized mixed equilibrium problem are investigated and a strong convergence theorem of common solutions is established in a non-uniformly convex Banach space.
Abstract: In this paper, a quasi-φ-nonexpansive mapping and a generalized mixed equilibrium problem are investigated. A strong convergence theorem of common solutions is established in a non-uniformly convex Banach space. The results presented in the paper improve and extend some recent results. c ©2016 All rights reserved.
TL;DR: In this article, the existence and uniqueness of solutions for coupled systems consisting from fractional differential equations of Riemann-Liouville type subject to coupled and uncoupled Hadamard fractional integral boundary conditions was studied.
Abstract: In this paper we study existence and uniqueness of solutions for coupled systems consisting from fractional differential equations of Riemann-Liouville type subject to coupled and uncoupled Hadamard fractional integral boundary conditions. The existence and uniqueness of solutions is established by Banach’s contraction principle, while the existence of solutions is derived by using Leray-Schauder’s alternative. Examples illustrating our results are also presented. c ©2016 All rights reserved.
TL;DR: A series of sufficient conditions for the existence and exponential stability of anti-periodic solutions to the neutral BAM neural networks with time-varying delays in the leakage terms are presented.
Abstract: This paper is concerned with the existence and exponential stability of anti-periodic solutions of a neutral BAM neural network with time-varying delays in the leakage terms. Using some analysis skills and Lyapunov method, a series of sufficient conditions for the existence and exponential stability of anti-periodic solutions to the neutral BAM neural networks with time-varying delays in the leakage terms are presented. Our results are new and complement some previously known ones. c ©2016 All rights reserved.
TL;DR: In this paper, the (k, s)-fractional integral operator is used to generate new classes of integral inequalities using a family of n positive functions, (n ∈ N).
Abstract: In this paper, the (k, s)-fractional integral operator is used to generate new classes of integral inequalities using a family of n positive functions, (n ∈ N). Two classes of integral inequalities involving the (k, s)fractional integral operator are derived here and these results allow us in particular to generalize some classical inequalities. Certain interesting consequent results of the main theorems are also pointed out. c ©2016 All rights reserved.
TL;DR: In this paper, based on the concepts of α-admissible mappings and simulation functions, the authors established some fixed point results in the setting of metric-like spaces and provided concrete examples to illustrate the obtained results.
Abstract: Based on concepts of α-admissible mappings and simulation functions, we establish some fixed point results in the setting of metric-like spaces. We show that many known results in the literature are simple consequences of our obtained results. We also provide some concrete examples to illustrate the obtained results. ©2016 All rights reserved.
TL;DR: In this article, a three-step iteration scheme for approximating fixed points of the nonlinear self mappings on a normed linear spaces satisfying Berinde contractive condition is introduced.
Abstract: The aim of this work is to introduce a new three step iteration scheme for approximating fixed points of the nonlinear self mappings on a normed linear spaces satisfying Berinde contractive condition. We also study the sufficient condition to prove that our iteration process is faster than the iteration processes of Mann, Ishikawa and Agarwal, et al. Furthermore, we give two numerical examples which fixed points are approximated by using MATLAB. c ©2016 All rights reserved.
TL;DR: In this article, the existence of solutions for a nonlinear Hadamard type fractional differential equation with strip condition and p-Laplacian operator was investigated under certain nonlinear growth conditions of the nonlinearity.
Abstract: Under certain nonlinear growth conditions of the nonlinearity, we investigate the existence of solutions for a nonlinear Hadamard type fractional differential equation with strip condition and p-Laplacian operator. At the end, two examples are given to illustrate our main results. ©2016 All rights reserved.