Some new existence results on the hybrid fractional differential equation with variable order derivative

Abstract

Fractional order systems play a vital role in the study of the abnormal behavior of dynamic systems in physics, biology, viscoelasticity, and in the study of population dynamics.The thing that caught our attention thinking about using the order of the fractional derivatives as a function, where we find some works (mentioned in the introduction), in which the order of the fractional derivative has been used as a function that changes with concentration, time, space, or other independent quantities.Motivated by these works in this manuscript, we studied the existence of solutions of the following hybrid fractional differential equation of variable order involving the ψ-Hilfer fractional derivative H t