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Abstract <p>In this work, the existence of solutions for boundary value problems involving nonlinear fractional <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(q\)</EquationSource> <!--LobJMat2561152Tokmagambetov-m3--> </InlineEquation>-difference equations is investigated. By applying methods from q-calculus and fractional differentiation theory, the original differential equation is reduced to an integral equation through the construction of a Green’s function. The existence of solutions is established using the Banach contraction principle, Krasnoselskii’s fixed point theorem, and the Leray–Schauder nonlinear alternative. Illustrative examples demonstrate the practical applicability of the obtained results.</p>

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On the Existence of Solutions to Boundary Value Problems for Nonlinear \(\boldsymbol{q}\)-Fractional Differential Equations

  • 期刊论文

  • 发表日期：

    2025年11月1日

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  • N. S. Tokmagambetov,
  • M. T. Kosmakova

摘要

Abstract

In this work, the existence of solutions for boundary value problems involving nonlinear fractional \(q\) -difference equations is investigated. By applying methods from q-calculus and fractional differentiation theory, the original differential equation is reduced to an integral equation through the construction of a Green’s function. The existence of solutions is established using the Banach contraction principle, Krasnoselskii’s fixed point theorem, and the Leray–Schauder nonlinear alternative. Illustrative examples demonstrate the practical applicability of the obtained results.