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An optimized numerical algorithm for nonlinear fractional differential equations involving the Caputo-Prabhakar derivative with convergence analysis
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F. Khoshsirat Chavary   , A. H. Refahi Sheikhani , M. Ilie |
| Department of Applied Mathematics, La.C., Islamic Azad University, Lahijan, Iran. |
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Abstract: (2 Views) |
In this paper, we introduce an optimized numerical scheme for solving nonlinear fractional differential equations involving the Caputo-Prabhakar derivative, which incorporates a memory kernel with a generalized Mittag-Leffler function. A new discretization based on convolution quadrature with accelerated kernel compression is developed to achieve optimal computational efficiency, and the resulting fully discrete implicit scheme is rigorously analyzed for stability and convergence. The theoretical convergence rate O(Δt2-λ+Δx2) is established for λ∈(1,2) via an energy method and discrete Grönwall inequality, confirming the optimal accuracy of the proposed approach. Numerical experiments are conducted to verify the theoretical findings, demonstrating excellent agreement with the exact solution and confirming the efficiency and optimal performance of the proposed algorithm. The results indicate that the optimized scheme is robust, accurate, and well-suited for long-time simulations of fractional models arising in engineering and physical sciences.
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| Keywords: Caputo-Prabhakar Derivative, Mittag-Leffler Function, Nonlinear Fractional Differential Equations, Convergence Analysis. |
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Full-Text [PDF 673 kb]
(2 Downloads)
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Type of Study: Research |
Subject:
General
Received: 2026/05/3 | Accepted: 2026/06/7 | Published: 2026/07/10
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