Title: Solving fuzzy fractional differential equations using fuzzy fractional fourth order Runge-Kutta method based on centroidal mean

Authors: S. Luvis Savla; R. Gethsi Sharmila

Addresses: PG and Research Department of Mathematics, Bishop Heber College, Trichy, Tamil Nadu, India; Affiliated to: Bharathidasan University, India ' PG and Research Department of Mathematics, Bishop Heber College, Trichy, Tamil Nadu, India; Affiliated to: Bharathidasan University, India

Abstract: In applied sciences and engineering, fuzzy fractional differential equations (FFDEs) are a crucial topic. The objective of this research is to determine the approximate solution to FFDEs. In the Caputo notion, the fractional derivatives are regarded. The fuzzy fractional fourth order Runge-Kutta method based on centroidal mean (FFRK4CeM) is developed to solve fuzzy fractional initial value problems (FFIVPs). The fuzzy fractional fourth-order Runge-Kutta method and the fuzzy fractional fourth-order Runge-Kutta method based on centroidal mean can be compared. Graphical results show the symmetry between the solutions' lower and upper μ-cut representations and satisfy the convex symmetric triangular fuzzy number. As the step size decreases, the approximate solution increasingly aligns with the result. Finally, the results indicate that the proposed method is user-friendly, precise, straightforward, and efficient for addressing both linear and nonlinear first-order finite initial value problems (FFIVP).

Keywords: Mittag-Leffler function; Caputo fractional derivative; fuzzy fractional differential equations; FFDEs; fuzzy fractional initial value problem; FFIVP; fuzzy fractional fourth order Runge-Kutta; FFRK4; fuzzy fractional fourth order Runge-Kutta method based on centroidal mean; FFRK4CeM; triangular fuzzy number; Zadeh's extension principle; linear triangular FFIVP; nonlinear triangular FFIVP.

DOI: 10.1504/IJANS.2025.148929

International Journal of Applied Nonlinear Science, 2025 Vol.5 No.1, pp.22 - 41

Received: 15 Jun 2023
Accepted: 10 Aug 2024
Published online: 04 Oct 2025 *

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