Analysis of mixed-order Caputo fractional system with nonlocal integral boundary condition

Abstract

This paper deals with a mixed-order Caputo fractional system with nonlocal integral boundary conditions. This study can be considered as an extension of previous studies, since the orders of the equations lie on different intervals. We discuss the existence and uniqueness of the solution using fixed point methods. We enrich the study with an example.

Analysis of boundary value problem with multi-point conditions involving Caputo-Hadamard fractional derivative

“…Apart from Riemann-Liouville and Caputo derivatives, the collected works have other types of fractional derivatives, which are Hadamard [10], known as Hadamard derivatives and vary from the previous ones as the logarithmic function of the arbitrary exponent is included in their definition. A detailed description of Hadamard fractional derivative and integral can be found in [2,1,7,14,16,29,28,25] and references cited therein. Note that the initial Hadamard type and BVPs are being investigated at their underlying level and need further consideration.…”