Approximate Solution of the Fuzzy Triangular Initial Value Problem with Different Fractional Operator

Abstract

This study aims to conduct a comparison regarding the process of solving the fuzzy triangular initial value problem (FTIVP). The series solution of this problem is acquired through the reproducing kernel theory (RKT), although there have been past studies on FTIVP, there is no specialist study to compare solutions for the definition of different fractional operator. The comparisons where located through the difference in the use of an operator in the process of solution by using Riemann-Liouville integral operator (RLIO) and then by using Caputo fractional derivative operator (CFDO). Algorithm was presented to validate the method of solution and to view the effect of changing the operators on the solution behaviour in the two cases. During this comparison, the effectiveness of RKT was cleared and the notion of difference between using RLIO and CFDO were fixedly identified. Applications: The results identified in this research pronounced active difference in the behavior of errors, CDFO variations, and the behavior of error in favour of RLIO.