Construction of Second- and Fourth-Order RK-Type Methods for Solving Fractional Differential Equations of the First Order

Discrete Dynamics in Nature and Society

卷:2026

Research Article

Elyas Arsanjani Toroqi¹  Seyed Reza Mirshafaei² 

[1] Department of Applied Mathematics and Computer Sciences, Lahijan Branch, Islamic Azad University, Lahijan, Iran, azad.ac.ir

[2] Department of Applied Mathematics, Roudsar and Amlash Branch, Islamic Azad University, Roudsar, Iran, azad.ac.ir

关键词: 26A33;    34A08;    65L06;    Caputo derivative;    conformable derivative;    conformable Runge–Kutta method (CRK);    fractional calculus;    fractional differential equations of the first order (FDEs of the first order);   

DOI  :  10.1155/ddns/7341891

 received in 2023-04-05, accepted in 2026-03-31,  发布年份 2026

来源: Hindawi Publishing Corporation

【 摘 要 】

In the present work, two distinct Runge–Kutta methods based on the conformable derivative were introduced for solving fractional differential equations of the first order. Both proposed methods were defined as second- and fourth-order and derived from Taylor series expansions and integral quadrature. Illustrative examples were discussed for the validity and efficiency of the methods. The absolute error graphs demonstrated the exceptional efficiency of the proposed methods and their greater accuracy than that of the conformable derivative. Furthermore, some approaches that provide more precise approximations than the fractional Runge–Kutta method were discovered.

【 授权许可】

CC BY   
Copyright © 2026 Elyas Arsanjani Toroqi and Seyed Reza Mirshafaei. Discrete Dynamics in Nature and Society published by John Wiley & Sons Ltd. 2026

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