On Some Fractional Problems

Résumé: The objective of this thesis is to give some existence results for various classes of initialvalue problem and boundary value problems for nonlinear fractional differential equationsand coupled system involving a various kind of fractional-order derivatives in Banach Spaces.For this purpose, the technique used is to reduce the study of our problem to the research ofa fixed point of an integral operator. The obtained results are based on some standard fixedpoint theorems and mönch fixed point theorem combined with the technique of measures ofnoncompactness, as well as the technique of topological degree theory. We have also provideda illustrative example to each of our considered problems to show the validity of conditionsand justify the efficiency of our established results.Key words and phrases :Fractional differential equation, Coupled fractional differentialsystem, Fractionalq-difference equation, Caputo fractional derivative, Caputo-Hadamardfractional derivative, Hilfer fractional derivative, fractionalq-derivative, boundary value pro-blems, initial value problem, Banach space, fixed-point, Kuratowski measure of noncompact-ness, existence, uniqueness, topological degree theory, condensing mapsAMS Subject Classification :26A33, 34A08, 34B15.

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