APPROXIMATIONS OF SOLUTIONS FOR A NONLOCAL FRACTIONAL INTEGRO-DIFFERENTIAL EQUATION WITH DEVIATED ARGUMENT

- Journal title : Journal of applied mathematics & informatics
- Volume 33, Issue 5_6, 2015, pp.699-721
- Publisher : The Korean Society of Computational and Applied Mathematics
- DOI : 10.14317/jami.2015.699

Title & Authors

APPROXIMATIONS OF SOLUTIONS FOR A NONLOCAL FRACTIONAL INTEGRO-DIFFERENTIAL EQUATION WITH DEVIATED ARGUMENT

CHADHA, ALKA; PANDEY, DWIJENDRA N.;

CHADHA, ALKA; PANDEY, DWIJENDRA N.;

Abstract

This paper investigates the existence of mild solution for a fractional integro-differential equations with a deviating argument and nonlocal initial condition in an arbitrary separable Hilbert space H via technique of approximations. We obtain an associated integral equation and then consider a sequence of approximate integral equations obtained by the projection of considered associated nonlocal fractional integral equation onto finite dimensional space. The existence and uniqueness of solutions to each approximate integral equation is obtained by virtue of the analytic semigroup theory via Banach fixed point theorem. Next we demonstrate the convergence of the solutions of the approximate integral equations to the solution of the associated integral equation. We consider the Faedo-Galerkin approximation of the solution and demonstrate some convergenceresults. An example is also given to illustrate the abstract theory.

Keywords

Analytic Semigroup;Banach fixed point Theorem;Caputo derivative;Neutral integro-differential equation;Faedo-Galerkin approximation;

Language

English

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