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

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

AIMS Mathematics, cilt.10, sa.6, ss.13231-13250, 2025 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 10 Sayı: 6
  • Basım Tarihi: 2025
  • Doi Numarası: 10.3934/math.2025593
  • Dergi Adı: AIMS Mathematics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Directory of Open Access Journals
  • Sayfa Sayıları: ss.13231-13250
  • Anahtar Kelimeler: convolution, Elzaki transform, fractional integrals, generalized fractional operators, graph modeling
  • Bursa Uludağ Üniversitesi Adresli: Evet

Özet

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.