Khalouta reduced differential transform method and its convergence for nonlinear fractional biological population equation under Caputo’s fractional operator

Hathat, Fatima; Khalouta, Ali

doi:10.47974/JIM-2101

Open Access Research Article

Khalouta reduced differential transform method and its convergence for nonlinear fractional biological population equation under Caputo’s fractional operator

Fatima Hathatfatima.hathat@univ-setif.dzDepartment of Mathematics Laboratory of Fundamental and Numerical Mathematics Faculty of Sciences Setif 1 University-Ferhat ABBAS AlgeriaView full profile → , ^*Ali KhaloutaCorresponding authornadjibkh@yahoo.fr; ali.khalouta@univ-setif.dzDepartment of Mathematics Laboratory of Fundamental and Numerical Mathematics Faculty of Sciences Setif 1 University-Ferhat ABBAS AlgeriaView full profile →

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pp. 2733–2750Vol. 28Issue 8December 2025DOI: 10.47974/JIM-2101XML

Received:: 06 Dec 2023
Published Online:: 09 Jun 2025
Article type:: Research Article
Language:: EN
Article no.:: JIM-2101
Pages:: 2733–2750

Abstract

The current paper focuses on finding the exact solution of the nonlinear fractional biological population equation under Caputo’s fractional operator by involving a new hybrid technique known as the Khalouta reduced differential transform method (KHRDTM). The exact solution is described in terms of the Mittag-Leffler functions. Moreover, the presented method is a powerful tool for solving a huge number of problems. The accuracy of the proposed technique is evaluated with the help of some examples and the results obtained are compared with the previous results of the techniques in the literature.

Keywords

Khalouta transform (KHT)Reduced differential transform method (RDTM)Caputo’s fractional derivative operator (CFDO)Riemann–Liouville fractional integral operator (RLFIO)Nonlinear fractional biological population equation (NFBPE)

Subject Classifications

26A3335R1135A2235C05

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