Work

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

Year: 2025

Type: article

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 $ \varrho $ 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 $ \varrho $ Riemann–Liouville, $ \varrho $ 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.

Source: AIMS Mathematics

DOI: 10.3934/math.2025593

Authors: Aysun Yurttas Gunes, Halim Benali, Mohammed Said Souid

Institutions: Bursa Uludağ Üni̇versi̇tesi̇, Université IBN Khaldoun Tiaret, Saveetha University

Language: English

Topic: Fractional Differential Equations Solutions

Subfield: Modeling and Simulation

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $1,200

OpenAlex ID: W4411166308