APPLICATION DE LA THEORIE DES OPERATEURS AU CALCUL FRACTIONNAIRE

Abstract

This thesis deals with operator theory and fractional calculus. We begin by introdu- cing new generalized metric spaces. Then, we prove some important properties of such new structures. We also apply xed point theory to establish some new results on contraction operators over the introduced generalized spaces. After that, we investigate the fractional calculus theory, where we will use integro-di¤erential operators as well as the di¤erential ones. We prove some recent results on the existence and uniqueness of solutions for some classes of fractional di¤erential equations and systems that have not been studied. Some generalized Fourier and Laplace transforms are also proved. Some analytic and numerical studies for fractional equations are also discussed.