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Existence, Uniqueness and Approximation of Solution for the Fractional Semilinear Integro-differential Equation

Alka Chadha, D. N. Pandey


In the present work, we consider a fractional order integro-differential equation in a separable Hilbert space H. Using an associated integral equation and projection operator, we study a sequence of approximate integral equations. We obtain the existence and uniqueness of the solution to every approximate integral equation by using semigroup theory and Banach fixed point theorem. We also show the convergence of the solutions of the approximate integral equations to the solution of the associated integral equation. At the last, we study the Faedo-Galerkin approximations of the solutions and demonstrate some convergence results.


Fractional differential equations, Analytic semigroup, Contraction mapping theorem, Approximate solution, Faedo-Galerkin approximation.

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