Existence results of nonlinear generalized proportional fractional differential inclusions via the diagonalization technique

Abstract

The present paper is concerned with the existence of solutions of a new class of nonlinear generalized proportional fractional differential inclusions with the right-hand side contains a Carathèodory-type multi-valued nonlinearity on infinite intervals. The investigation of the proposed inclusion problem relies on the multi-valued form of Leray-Schauder nonlinear alternative incorporated with the diagonalization technique. By specializing the parameters involved in the problem at hand, an illustrated example is proposed.

Keywords

• fractional differential inclusions
• generalized proportional fractional derivatives
• diagonalization method
• carathèodory multi-valued maps