Existence Results for Fractional Hahn Difference and Fractional Hahn Integral Boundary Value Problems

Abstract

The existence and uniqueness results of two fractional Hahn difference boundary value problems are studied. The first problem is a Riemann-Liouville fractional Hahn difference boundary value problem for fractional Hahn integrodifference equations. The second is a fractional Hahn integral boundary value problem for Caputo fractional Hahn difference equations. The Banach fixedpoint theorem and the Schauder fixed-point theorem are used as tools to prove the existence and uniqueness of solution of the problems.

Impulsive fractional quantum Hahn difference boundary value problems

“…Theorem 4 Let f and ϕ k be given functions satisfying (19) and (20), respectively, for all k = 1, 2, . .…”

“…[11][12][13][14]). For some recent results on the boundary value problems of Hahn difference equations we refer to [15][16][17][18][19] and references therein. Let us emphasize that the definition (3) does not remain valid for impulse points t k , k ∈ Z, such that t k ∈ (qt, t).…”

Some results on quantum Hahn integral inequalities

“…[3][4][5][6]). For some recent results to boundary value problems for Hahn difference operators, we refer to papers [7][8][9][10] and the references cited therein. Let [a, b] ⊆ R be an interval.…”

On nonlocal Robin boundary value problems for Riemann–Liouville fractional Hahn integrodifference equation

“…In 2017, Patanarapeelert and Sitthiwirattham [34] considered a Riemann-Liouville fractional Hahn difference boundary value problem for a fractional Hahn integrodifference equation of the form…”

“…In quantum calculus, there are apparently few research works related to boundary value problems of fractional Hahn difference equations (see [34,35] …”