Numerical solution for fuzzy fractional differential equations using fuzzy fractional fourth order Runge-Kutta method based on root mean square and contraharmonic mean

Gethsi Sharmila R, Luvis Savla S

Abstract


The objective of this research is to determine the approximate solu[1]tion to Fuzzy Fractional Differential Equations (FFDEs). For Fuzzy Fractional Initial Value Problems (FFIVPs), the methods called Fuzzy Fractional Fourth Order Runge-Kutta method based on Root Mean Square (FFRK4RM) and called Fuzzy Fractional Fourth Order Runge[1]Kutta method based on Contraharmonic Mean (FFRK4CoM) is de[1]veloped. In this paper, both linear and nonlinear FFDEs can be solved using triangular and trapezoidal fuzzy numbers. FFRRK4RM and FFRK4CoM can be compared. The tables gives the absolute error between the exact and approximate solutions. From the graphical results, the approximate solution approaches the exact result very closely as the step size gets smaller. The outcomes show that the suggested approach is easy to use, accurate, clear, and convenient for solving both linear and nonlinear FFIVP.


Keywords


FFRK4RM, FFRK4CoM, FFDEs, Triangular fuzzy num ber, Trapezoidal fuzzy number

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DOI: http://dx.doi.org/10.23755/rm.v49i0.1429

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