Analysis on existence of system of coupled multifractional nonlinear hybrid differential equations with coupled boundary conditions

Abstract

This article dealt with a class of coupled hybrid fractional differential system. It consisted of a mixed type of Caputo and Hilfer fractional derivatives with respect to two different kernel functions, $ \psi_{_1} $ and $ \psi_{_2} $, respectively, in addition to coupled boundary conditions. The existence of the solution of the system was investigated using the Dhage fixed point theorem. Finally, an illustration was presented to validate our findings.

Keywords

• $ \psi $-hilfer and $ \psi $-caputo fractional derivatives
• hybrid fractional differential equations
• fixed point theory
• existence