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Existence and approximations of solutions to some fractional order functional integral equations

Muslim, M and Nandakumaran, K (2010) Existence and approximations of solutions to some fractional order functional integral equations. In: Journal of Integral Equations and Applications, 22 (1). pp. 95-114.

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Abstract

In this paper we shall study a fractional order functional integral equation. In the first part of the paper, we proved the existence and uniqueness of mile and global solutions in a Banach space. In the second part of the paper, we used the analytic semigroups theory oflinear operators and the fixed point method to establish the existence, uniqueness and convergence of approximate solutions of the given problem in a separable Hilbert space. We also proved the existence and convergence of Faedo-Galerkin approximate solution to the given problem. Finally, we give an example.

Item Type: Journal Article
Additional Information: Copyright of this article belongs to Rocky Mountain Mathematics Consortium.
Keywords: Fractional order functional integral equations;Banach fixed point theorem;analytic semi-group;mild solution;global solution;Faedo-Galerkin approximation
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Date Deposited: 09 Jun 2010 05:15
Last Modified: 17 Aug 2010 10:03
URI: http://eprints.iisc.ernet.in/id/eprint/27252

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