FRACTIONAL DIFFERENTIAL EQUATIONS IN NONREFLEXIVE BANACH SPACES

Abstract

This thesis is devoted to fractional calculus in nonreflexive Banach spaces and exis- tence results for the fractional differential equations. Using fractional Pettis integral and fractional pseudo-derivative, we discussed fractional calculus and fractional dif- ferential equations in nonreflexive Banach spaces, equipped with weak topology. We obtained some results on existence of solution of fractional differential equations. Furthermore, applying fractional Pettis integral and fractional pseudo-derivative we discussed the existence of solution of multi-term fractional differential equation, in nonreflexive Banach spaces, equipped with weak topology. Finally, assuming the concept of Riemann-Pettis integral, we introduced and studied the notions of frac- tional Riemann-Pettis integral and fractional Caputo weak derivative. Using these tool we obtained an existence result for weak solution of fractional differential equa- tions in a nonreflexive Banach space equipped with the weak topology.