Chapters authored
A Study of Nonlinear Boundary Value Problem
In this chapter, firstly we apply the iterative method to establish the existence of the positive solution for a type of nonlinear singular higher-order fractional differential equation with fractional multi-point boundary conditions. Explicit iterative sequences are given to approximate the solutions and the error estimations are also given. Secondly, we cover the multi-valued case of our problem. We investigate it for nonconvex compact valued multifunctions via a fixed point theorem for multivalued maps due to Covitz and Nadler. Two illustrative examples are presented at the end to illustrate the validity of our results.
Part of the book: Simulation Modeling
A Study for Coupled Systems of Nonlinear Boundary Value Problem
This chapter deals with the existence and uniqueness of solutions for a coupled system of fractional differential equations with coupled nonlocal and integral boundary conditions and for the system of two-point boundary value problem when we take the case of integer derivative. The existence results for the fist problem are obtained by using Leray-Shauder nonlinear alternative and Banach contraction principle and for the second problem, we derive explicit eigenvalue intervals of λ for the existence of at least one positive solution by using Krasnosel’skii fixed point theorem. An illustrative examples is presented at the end for each problem to illustrate the validity of our results.
Part of the book: Boundary Layer Flows
Existence Results for Boundary Value Problem of Nonlinear Fractional Differential Equation
In this chapter, we investigate the existence and uniqueness of solutions for class of nonlinear fractional differential equations with nonlocal boundary conditions. The existence results are obtained by using Leray-Schauder nonlinear alternative and Banach contraction principle. An illustrative example is presented at the end to illustrated the validity of our results.
Part of the book: Nonlinear Systems