A New Class of $\psi$-Caputo Fractional Differential Equations and Inclusion

Abstract

In the present research work, we investigate the existence of a solution for new boundary value problems involving fractional differential equations with ψ -Caputo fractional derivative supplemented with nonlocal multipoint, Riemann–Stieltjes integral and ψ -Riemann–Liouville fractional integral operator of order γ boundary conditions. Also, we study the existence result for the inclusion case. Our results are based on the modern tools of the fixed-point theory. To illustrate our results, we provide examples.

Existence of solutions to boundary value problems for a class of infinite point fractional q-difference equations

“…With the continuous research on fractional differential equations by researchers, fractional differential equations have been developed rapidly in recent decades, and many scientific research achievements have also been made [1,3,8]. In recent years, some scholars have introduced the ideas and methods of fractional differential equations into the study of fractional q-difference equations, and also made some research achievements [2,4,5,6,9,10]. However, the definition of fractional order q-difference equation is more complex, so it is difficult to judge the solution of boundary value problems, especially in the study of the properties of Green function.…”