Nonlinear fractional differential inclusion with nonlocal fractional integro-differential boundary conditions in Banach spaces. (English) Zbl 06770148

Seba, Djamila

Math. Bohem. 142, No. 3, 309-321 (2017).

Summary: We consider a nonlinear fractional differential inclusion with nonlocal fractional integro-differential boundary conditions in a Banach space. The existence of at least one solution is proved by using the set-valued analog of Mönch fixed point theorem associated with the technique of measures of noncompactness.

MSC:

34	Ordinary differential equations
26A33	Fractional derivatives and integrals
34A60	Ordinary differential inclusions
34B15	Nonlinear boundary value problems for ordinary differential equations

Keywords:

differential inclusion; Caputo fractional derivative; nonlocal boundary conditions; Banach space; existence; fixed point; measure of noncompactness