SOME NEW RESULTS ON NONLINEAR FRACTIONAL ITERATIVE VOLTERRA-FREDHOLM INTEGRO DIFFERENTIAL EQUATIONS

SOME NEW RESULTS ON NONLINEAR FRACTIONAL ITERATIVE VOLTERRA-FREDHOLM INTEGRO DIFFERENTIAL EQUATIONS

A. A. Hamoud, K. P. Ghadle

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Abstract

In this paper, we establish some new results concerning the existence and uniqueness of the solutions of iterative nonlinear Volterra-Fredholm integro di erential equations subject to the initial conditions. The fractional derivatives are considered in the Caputo sense. Also these new results are obtained by applying the Gronwall- Bellman's inequality and the Banach contraction  xed point theorem. Moreover, the results of references [16, 17, 27] appear as a special case of our results.

Keywords

Volterra-Fredholm integro-di erential equation, Caputo sense, Gronwall- Bellman's inequality, Banach contraction  xed point theorem.