On multi-term proportional fractional differential equations and inclusions

Abstract

Abstract The aim of this paper is to study new nonlocal boundary value problems of fractional differential equations and inclusions supplemented with slit-strips integral boundary conditions. Based on the functional analysis tools, the existence results for a nonlinear boundary value problem involving a proportional fractional derivative are presented. In addition to that, the extension of the problem at hand to its inclusion case is discussed. The obtained results are very interesting and are well illustrated with examples.

Keywords

• Generalized fractional integral
• Generalized proportional derivative
• Fixed point theorem