AN EXISTENCE RESULT FOR MULTI-TERM FRACTIONAL INTEGRO-DIFFERENTIAL INCLUSIONS VIA NONLINEAR ALTERNATIVE FOR MULTI-VALUED CONTRACTIVE MAPS

In this paper, by applying nonlinear alternative for multi-valued contractive maps, we establish an existence result for a new class of boundary value problems consisting of a nonlinear multi-term fractional integro-differential inclusion involving Caputo derivatives supplemented with non-separated nonlocal integromultipoint boundary conditions. The obtained result is well illustrated by a numerical example. Several new results appear as special cases of the main result.

Automated summary

In this paper, an existence result is established for a new class of boundary value problems involving a nonlinear multi-term fractional integro-differential inclusion with Caputo derivatives and non-separated nonlocal integromultipoint boundary conditions, by applying a nonlinear alternative for multi-valued contractive maps. The obtained result is well illustrated by a numerical example and several new results appear as special cases of the main result.