The nonlocal Cauchy problem for nonlinear fractional integrodifferential equations in Banach spaces

On the existence of solutions of fractional integro-differential equations

“…We will mention some of they. In [5]- [7], Balachandran et al proved the existence of solutions of integro-differential equations in Banach spaces. Also, we can find existence results for boundary value problems of fractional differential equations in the survey by Agarwal et al [2] and in the papers [1], [10], [14], and [32].…”

On the solutions of partial integrodifferential equations of fractional order

“…There are few articles available in the literature for the study of fractional integrodierential equations. For example, Balachandran et al [4,5] studied the existence results for several kinds of fractional integrodierential equations in a Banach space using xed point technique. In [32], Zhang et al investigated the existence of nonnegative solutions for nonlinear fractional dierential equations with nonlocal fractional integrodierential boundary conditions on an unbounded domain by using the Leray-Schauder nonlinear alternative theorem.…”

Fractional evolution equation nonlocal problems with noncompact semigroups

“…Since it is demonstrated that the nonlocal problems have are better in applications than the traditional Cauchy problems, differential equations with nonlocal conditions were studied by many authors and some basic results on nonlocal problems have been obtained, see [2,3,[6][7][8]10,13,17,21,22,29,31,32] and the references therein.…”