On the generalized Elzaki transform and its applications to fractional differential equations

YURTTAŞ GÜNEŞ A., Benali H., Souid M. S.

AIMS Mathematics, vol.10, no.6, pp.13231-13250, 2025 (SCI-Expanded, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 10 Issue: 6
  • Publication Date: 2025
  • Doi Number: 10.3934/math.2025593
  • Journal Name: AIMS Mathematics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Directory of Open Access Journals
  • Page Numbers: pp.13231-13250
  • Keywords: convolution, Elzaki transform, fractional integrals, generalized fractional operators, graph modeling
  • Bursa Uludag University Affiliated: Yes

Abstract

In this paper, we introduce a modified Elzaki transform and its generalization, namely the Elzaki transform, and its own convolution theorem is given. These generalization are given by composition with a monotonic increasing function ϱ having a continuous derivative. A revised version of the Elzaki transform that is broader in scope and applicable over a wider range is developed, and some of its fundamental properties are given. This modified transform is performed to find solutions of certain non homogeneous linear ϱ Riemann–Liouville, ϱ Caputo fractional differential equations. Using comparision graphs, one can determine the effectiveness of the solutions. This research opens up new avenues for future research and has the potential to make a significant impact on the field of mathematics and its applications.