On four-point fractional q-integrodifference boundary value problems involving separate nonlinearity and arbitrary fractional order

In this paper, we study a sequential Caputo fractional q-integrodifference equation with fractional q-integral and Riemann–Liouville fractional q-derivative boundary value conditions. Our problem contains 2(M+N+1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$2(M+N+1)$\end{document} different orders and six different numbers of q in derivatives and integrals. The problem contains separate nonlinear functions. To examine existence and uniqueness results of the problem, Banach’s contraction principle and the Leray–Schauder nonlinear alternative are employed. An illustrative example is also provided.