Work

On the solutions of fractional differential equations with modified Mittag-Leffler kernel and Dirac Delta function: Analytical results and numerical simulations

Year: 2025

Type: article

Abstract: In this paper we define, for the first time, the modified fractional derivative with Mittage-Leffler kernel of Riemann-Liouville (R-L) type of arbitrary order [Formula: see text]delta. We derive the infinite series representations for the modified derivatives of R-L and Caputo types and present a relationship between them. We also investigate the modified derivatives for the Dirac delta functions, and study related fractional differential equations. Explicit solutions were presented for linear fractional differential equations with constant coefficients via the Laplace transform. A fractional model with the modified derivative is considered and numerical simulations were presented.

Source: PLoS ONE

DOI: 10.1371/journal.pone.0325897

Authors: Mohammed Al-Refai, Dumitru Baleanu, A.K. Alomari

Institutions: Yarmouk University, Institute of Space Science - INFLPR Subsidiary, Lebanese American University, Islamic University of Madinah

Language: English

Topic: Fractional Differential Equations Solutions

Subfield: Modeling and Simulation

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,382

OpenAlex ID: W4411401727

FWCI: 1.489

Cites: 24

Cited by: 2

Related to: 10