A novel technique for solving the fractional Phi-four formula

Alsaadi, Ahmed Amer; Ellouze, Ines

doi:10.47974/JIM-1982

Open Access Research Article

A novel technique for solving the fractional Phi-four formula

^*Ahmed Amer AlsaadiCorresponding authorAhmed11math@gmail.comGeneral Directorate of Coordination & Follow up, Ministry of Youth & SportsBaghdad, IraqView full profile → , Ines Ellouzeinesellouze@yahoo.frDepartment of MathematicsFaculty of Sciences of SfaxUniversity of SfaxSfax, TunisiaView full profile →

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pp. 847–858Vol. 28Issue 3-AApril 2025DOI: 10.47974/JIM-1982XML

Received:: 08 May 2024
Published Online:: 08 May 2025
Article type:: Research Article
Language:: EN
Article no.:: JIM-1982
Pages:: 847–858

Abstract

This study presents an enhanced analytical approximation method for solving the fractional Phi-four formula. We offer an alternate foundation for applying the LRPS technique to handle fractional differentiation problems that arise in many physical occurrences. This technique is based on residue function and the expanded Taylor series formula. The suggested course of action produces favorable results. The robustness, effectiveness, and ease of use of the proposed approach are demonstrated for all classes of fractional issues that arise in the analytical and technical areas. The efficiency of the suggested method in resolving numerous types of fractional differential equations is demonstrated with a case study. The case study provides empirical proof that the recommended method works well for solving a variety of issues involving fractions. Finally, compared to existing methods like q-HATM and HAM, our approach yields effective and favorable outcomes

Keywords

Analytical approximations Fractional calculus Fractional Phi-four formula Ordinary differential equations

Subject Classifications

Primary 34A25Secondary 11J54

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