Solutions of sum-type singular fractional q integro-differential equation with m-point boundary value problem using quantum calculus

Abstract

Nowadays, many researchers have considerable attention to fractional calculus as a useful tool for modeling of different phenomena in the world. In this work, we investigate the sum-type singular nonlinear fractional q integro-differential equations with m-point boundary value problem. The existence of positive solutions is obtained by the properties of the Green function, standard Caputo q derivative, Riemann–Liouville fractional q integral, and a fixed point theorem on a real Banach space (Formula presented.), which has a partial order by using a cone (Formula presented.). The proofs are based on solving the operators equation. By providing seven algorithms, four tables, and three figures, we give two numerical examples to illustrate our main result. © 2020 Elsevier B.V., All rights reserved.