Solutions of fractional partial differential equations by combined new technique NTADM

Abdulhadi, Ahmed Najah; Altaie, Huda Omran

doi:10.47974/JIM-2543

Open Access Research Article

Solutions of fractional partial differential equations by combined new technique NTADM

^*Ahmed Najah AbdulhadiCorresponding authorahmed.abd2203@ihcoedu.uobaghdad.edu.iqDepartment of Mathematics College of Education for Pure Science (Ibn Al-Haitham) University of BaghdadDepartment of Mathematics College of Education for Pure Science (Ibn Al-Haitham) University of BaghdadBaghdad, 10071, IraqView full profile → , Huda Omran Altaiehuda.h.o@ihcoedu.uobaghdad.edu.iqDepartment of Mathematics College of Education for Pure Science (Ibn Al-Haitham) University of BaghdadDepartment of Mathematics College of Education for Pure Science (Ibn Al-Haitham) University of Baghdad Baghdad, 10071, IraqView full profile →

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pp. 1683–1688Vol. 29Issue 5-BMay 2026DOI: 10.47974/JIM-2543XML

Received:: 01 Nov 2025
Published Online:: 27 Jun 2026
Article type:: Research Article
Language:: EN
Article no.:: JIM-2543
Pages:: 1683–1688

Abstract

An application of fractional differential equations is on the rise across physics, biology, and engineering. This is especially true when standard integer-order models fail to adequately describe a given phenomenon. A large number of practical systems rely on these equations, which enable the accounting for memory and nonlocal effects. But the mathematical complexity of high-order fractional models makes them difficult to address. To approximate solutions to these kinds of problems, this research employs the Adomian Decomposition Method in combination with the Natural Transform. The fractional derivatives are transformed to algebraic expressions using the Natural Transform, and nonlinear terms are systematically treated using the Adomian technique. This method is validated for fractional differential equations by the numerical results obtained for fractional orders between 4.7 and 4.9, which show that stable solutions with absolute errors less than one are produced.

Keywords

Natural transform Analytical technique Fractional order High-order fractional models

Subject Classifications

35R1135R60

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