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q-Sumudu Transform: Theory and Applications

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  • Rahmatullah Qarloq
  • Fatma Hıra

Abstract

In this paper, we introduce a new integral definition for the q-Sumudu transform that addresses earlier convergence issues and mirrors the classical version more naturally when q → 1−. Along with this definition, we establish a series form based on q-Taylor expansions and analyze the q-analogues of several key functions and theorems. Finally, we demonstrate the practical value of this approach by using our proposed transform to find analytical solutions for specific q-differential equations, which are typically difficult to solve using standard methods.

Suggested Citation

  • Rahmatullah Qarloq & Fatma Hıra, 2026. "q-Sumudu Transform: Theory and Applications," European Journal of Mathematics and Statistics, European Open Science, vol. 7(4), pages 1-7, November.
    • Handle: RePEc:epw:ejmath:v:7:y:2026:i:4:id:70729
    DOI: 10.24018/ejmath.2026.7.4.70729
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