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.