USING RELIABLE TECHNIQUES TO SOLVE NONLINEAR FRACTIONAL DIFFERENTIAL EQUATIONS ALONG WITH THEORETICAL ANALYSIS

Nazek A. Obeidat; Mohannad E. Alkhamaiseh; Mahmoud S. Rawashdeh

doi:10.11948/20250117

2026 Volume 16 Issue 1

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Nazek A. Obeidat, Mohannad E. Alkhamaiseh, Mahmoud S. Rawashdeh. USING RELIABLE TECHNIQUES TO SOLVE NONLINEAR FRACTIONAL DIFFERENTIAL EQUATIONS ALONG WITH THEORETICAL ANALYSIS[J]. Journal of Applied Analysis & Computation, 2026, 16(1): 76-98. doi: 10.11948/20250117

Citation:

Nazek A. Obeidat, Mohannad E. Alkhamaiseh, Mahmoud S. Rawashdeh. USING RELIABLE TECHNIQUES TO SOLVE NONLINEAR FRACTIONAL DIFFERENTIAL EQUATIONS ALONG WITH THEORETICAL ANALYSIS[J]. Journal of Applied Analysis & Computation, 2026, 16(1): 76-98. doi: 10.11948/20250117

USING RELIABLE TECHNIQUES TO SOLVE NONLINEAR FRACTIONAL DIFFERENTIAL EQUATIONS ALONG WITH THEORETICAL ANALYSIS

1.
Department of Mathematics and Statistics, Jordan University of Science and Technology, P. O. Box 3030, 22110 Irbid, Jordan

Author Bio: Email: obeidatnazek@gmail.com(N. A. Obeidat); Email: mealkhamaiseh21@sci.just.edu.jo(M. E. Alkhamaiseh)
Corresponding author: msalrawashdeh@just.edu.jo(M. S. Rawashdeh)

Abstract

Abstract

Throughout the current work, we implement a novel method to provide exact and approximate solutions, called the fractional $ \mathcal{J}- $transform Adomian decomposition method ($ \mathcal{FJADM} $). The suggested technique is used to explore solutions to the nonlinear time-fractional diffusion, Harry-Dym, and Fisher equations, including their theoretical analysis. We present detailed proofs of the existence and uniqueness theorems applied to nonlinear fractional ODEs using the $ \mathcal{FJADM} $. We combined in this work both the $ \mathcal{J} $-transform method ($ \mathcal{JTM} $) and the Adomian decomposition method (ADM). Clearly, from the results obtained, the new scheme proposed in this work is highly accurate and efficient. The results have shown how powerful and effective this method is and how straightforward it is for solving many types of fractional differential equations. The numerical calculations in the current work were carried out using Mathematica 13.
- Caputo fractional derivative /
- Adomian decomposition method /
- J-transform method /
- Harry-Dym equation /
- Banach fixed point theorem.
MSC: 26A33,34A08,34C60,35R11,26A33,92D30

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