Generalized Caputo Fractional Proportional Differential Equations and Inclusion Involving Slit-Strips and Riemann-Stieltjes Integral Boundary Conditions

Abstract

The main purpose of this study is to investigate the existence and uniqueness of solutions to a nonlocal boundary value problem. This newly defined class involves nonlinear fractional differential equations of general proportional fractional derivative and integral with respect to another function. Additionally, the inclusion case results associated to our problem are discussed. Our analysis relies on fixed point theorems and fractional calculus techniques. By giving examples, the obtained results are clearly illustrated.