DOI: 10.12732/ijam.v38i3.4
REGULARIZED ITERATIVE FDEM:
A NUMERICAL APPROACH FOR
NONLINEAR CAPUTO FRACTIONAL
DIFFERENTIAL EQUATIONS
Ramzi Albadarneh 1, Iqbal M. Batiha 2,3,§, Radwan M. Batyha 4, Shaher Momani 3,5
1 Department of Mathematics, The Hashemite University
Zarqa 13133, JORDAN
2 Department of Mathematics
Al Zaytoonah University of Jordan
Amman 11733, JORDAN
3 Nonlinear Dynamics Research Center (NDRC)
Ajman University, Ajman, UAE
4 Department of Computer Science
Applied Science Private University
Amman 11931, JORDAN
5 Department of Mathematics, University of Jordan
Amman 11931, JORDAN
Abstract. In this paper, we propose a novel numerical technique – Regularized Iterative Fractional Differential Equation Method (FDEM) - for solving nonlinear fractional differential equations (FDEs) involving the Caputo derivative. The method begins by reformulating the fractional Differential equation as a Volterra integral equation and addresses the weak singularity in the kernel by a regularization strategy that decomposes the nonlinear term. This decomposition enables a stable and accurate numerical integration using the composite trapezoidal rule. To handle the nonlinearity, a fixed-point iteration is employed at each time step. The resulting algorithm is simple to implement, computationally efficient with O(m^2) complexity, and adaptable to various types of nonlinear FDEs. The method’s stability, accuracy, and flexibility make it suitable for practical applications, including systems of fractional equations and higher-dimensional problems. For validating the robustness and effectiveness of the established approach, numerous numerical problems are addressed.
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DOI: 10.12732/ijam.v38i3.4
Source: International Journal of Applied Mathematics
ISSN printed version: 1311-1728
ISSN on-line version: 1314-8060
Year: 2025
Volume: 38
Issue: 3
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