Existence results for nonlocal boundary value problems of nonlinear fractional q-difference equations

By Bashir Ahmad, Sotiris K. Ntouyas, I. Purnaras. Advances in Differential Equations, 2012

117 citations recorded by the source corpus.

In this paper, we study a nonlinear fractional q-difference equation with nonlocal boundary conditions. The existence of solutions for the problem is shown by applying some well-known tools of fixed-point theory such as Banach’s contraction principle, Krasnoselskii’s fixed-point theorem, and the Leray-Schauder nonlinear alternative. Some illustrating examples are also discussed. MSC:34A08, 39A05, 39A12, 39A13.

Subfields: Applied Mathematics, Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/890c146b04dedea4a28cc55bcfad7deb3b56e5f9

Citations in the corpus

• Existence Theory for a Fractional q-Integro-Difference Equation with q-Integral Boundary Conditions of Different Orders (2019, unknown): “[11] discussed the existence and uniqueness of solutions for the nonlocal boundary value problem of fractional q-difference equations: { cDα q x(t) = f (t, x(t)), 0 ≤ t ≤ 1, 1 < α ≤ 2, 0 < q < 1, α1x(0)− β1Dqx(0) = γ1x(η1), α2x(1)− β2Dqx(1) = γ2x(η2), where f ∈ C([0, 1]×R,R), cDα q is the fractional”