Fractal and Fractional (Jan 2024)

Positive Solutions for a System of Fractional <i>q</i>-Difference Equations with Multi-Point Boundary Conditions

  • Rodica Luca

DOI
https://doi.org/10.3390/fractalfract8010070
Journal volume & issue
Vol. 8, no. 1
p. 70

Abstract

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We explore the existence, uniqueness, and multiplicity of positive solutions to a system of fractional q-difference equations that include fractional q-integrals. This investigation is carried out under coupled multi-point boundary conditions featuring q-derivatives and fractional q-derivatives of various orders. The proofs of our principal findings employ a range of fixed-point theorems, including the Guo–Krasnosel’skii fixed-point theorem, the Leggett–Williams fixed-point theorem, the Schauder fixed-point theorem, and the Banach contraction mapping principle.

Keywords