Fractional Differential Equations

nonlinear functional analysis and its applications is available in our book collection an online access to it is set as public so you can get it instantly. Our books collection hosts in multiple countries, allowing you to get the most less latency time to download any of our books like this one. Merely said, the nonlinear functional analysis and its applications is universally compatible with any devices to read.

Nonlinear Functional Analysis And Its Applications

The work is giving estimations of the discrepancy between solutions of the initial and the homogenized problems for a one{dimensional second order elliptic operators with random coeecients satisfying strong or uniform mixing conditions. We obtain several sharp estimates in terms of the corresponding mixing coeecient. Abstract. In the theory of homogenisation it is of particular interest to determine the classes of problems which are stable on taking the homogenisation limits. A notable situation where the limit enlarges the class of original problems is known as memory (nonlocal) eeects. A number of results in that direction has been obtained for linear problems. Tartar (1990) innitiated the study of the eeective equation corresponding to nonlinear equation: @ t u n + a n u 2 n = f: Signiicant progress has been hampered by the complexity of required computations needed in order to obtain the terms in power{series expansion. We propose a method which overcomes that diiculty by introducing graphs representing the domain of integration of the integrals in each term. The graphs are relatively simple, it is easy to calculate with them and they give us a clear image of the form of each term. The method allows us to discuss the form of the eeective equation and the convergence of power{series expansions. The feasibility of our method for other types of nonlinearities will be discussed as well.

Applied Mathematics and Computation

computational fluid mechanics and heat transfer is available in our book collection an online access to it is set as public so you can download it instantly. Our digital library hosts in multiple countries, allowing you to get the most less latency time to download any of our books like this one. Kindly say, the computational fluid mechanics and heat transfer is universally compatible with any devices to read.

Computational Fluid Mechanics And Heat Transfer

The cable equation plays a central role in many areas of electrophysiology and in modeling neuronal dynamics. This paper reports an accurate spectral collocation method for solving one- and two-dimensional variable-order fractional nonlinear cable equations. The proposed method is based on shifted Jacobi collocation procedure in conjunction with the shifted Jacobi operational matrix for variable-order fractional derivatives, described in the sense of Caputo. The main advantage of the proposed method is to investigate a global approximation for spatial and temporal discretizations. In addition, the method reduces the variable-order fractional nonlinear cable equation to a simpler problem that consists of solving a system of algebraic equations. The validity and effectiveness of the method are demonstrated by solving three numerical examples. The convergence of the method is graphically analyzed. The results demonstrate that the proposed method is a powerful algorithm with high accuracy for solving the variable-order nonlinear partial differential equations.

Numerical simulation for two-dimensional variable-order fractional nonlinear cable equation

The authors study a type of nonlinear fractional boundary value problem with non-homogeneous integral boundary conditions. The existence and uniqueness of positive solutions are discussed. An example is given as the application of the results.

Uniqueness of positive solutions of fractional boundary value problems with non-homogeneous integral boundary conditions

In this paper, the authors consider a nonlinear fractional boundary value problem defined on a star graph. By using a transformation, an equivalent system of fractional boundary value problems with mixed boundary conditions is obtained. Then the existence and uniqueness of solutions are investigated by fixed point theory.

/pdf/existence-and-uniqueness-of-solutions-for-a-fractional-303j5pcq8f.pdf

Existence and uniqueness of solutions for a fractional boundary value problem on a graph

In this article, we study a type of nonlinear fractional boundary value problem with integral boundary conditions. By constructing an associated Green's function, applying spectral theory and using fixed point theory on cones, we obtain criteria for the existence, multiplicity and nonexistence of positive solutions.

Fractional boundary value problems with integral boundary conditions

The authors consider a nonlinear fractional boundary value prob- lem with the Dirichlet boundary condition. An associated Green's function is constructed as a series of functions by applying spectral theory. Criteria for the existence and uniqueness of solutions are obtained based on it.

/pdf/existence-and-uniqueness-of-solutions-for-a-fractional-2dd5tuqku1.pdf

Min Wang

Papers

Uniqueness of positive solutions of fractional boundary value problems with non-homogeneous integral boundary conditions

Existence and uniqueness of solutions for a fractional boundary value problem on a graph

Fractional boundary value problems with integral boundary conditions

Existence and uniqueness of solutions for a fractional boundary value problem with dirichlet boundary condition

A Chebyshev spectral method for solving Riemann-Liouville fractional boundary value problems