Discrete Fractional Boundary Value Problems and Inequalities

• Published in: Fractional calculus & applied analysis Vol. 24; no. 6; pp. 1777 - 1796
• Main Authors: Bohner, Martin, Fewster-Young, Nick
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 01.12.2021; De Gruyter; Nature Publishing Group
• Subjects: 39A12; 39A27; 39A70; Abstract Harmonic Analysis; Analysis; boundary value problem; Boundary value problems; discrete fractional calculus; discrete fractional inequalities; existence of solutions; Existence theorems; Fixed points (mathematics); Functional Analysis; Inequalities; Integral Transforms; Mathematics; Operational Calculus; Primary 26A33; Research Paper; Secondary 34A08; Primary 26A33; discrete fractional calculus; 39A12; existence of solutions; 39A27; boundary value problem; discrete fractional inequalities; 39A70; Secondary 34A08

In this paper, a general nonlinear discrete fractional boundary value problem is considered, of order between one and two. The main result is an existence theorem, proving the existence of at least one solution to the boundary value problem, subject to validity of a certain key inequality that allow...