Series Representations for Uncertain Fractional IVPs in the Fuzzy Conformable Fractional Sense

Abstract

Fuzzy differential equations provide a crucial tool for modeling numerous phenomena and uncertainties that potentially arise in various applications across physics, applied sciences and engineering. Reliable and effective analytical methods are necessary to obtain the required solutions, as it is very difficult to obtain accurate solutions for certain fuzzy differential equations. In this paper, certain fuzzy approximate solutions are constructed and analyzed by means of a residual power series (RPS) technique involving some class of fuzzy fractional differential equations. The considered methodology for finding the fuzzy solutions relies on converting the target equations into two fractional crisp systems in terms of ρ-cut representations. The residual power series therefore gives solutions for the converted systems by combining fractional residual functions and fractional Taylor expansions to obtain values of the coefficients of the fractional power series. To validate the efficiency and the applicability of our proposed approach we derive solutions of the fuzzy fractional initial value problem by testing two attractive applications. The compatibility of the behavior of the solutions is determined via some graphical and numerical analysis of the proposed results. Moreover, the comparative results point out that the proposed method is more accurate compared to the other existing methods. Finally, the results attained in this article emphasize that the residual power series technique is easy, efficient, and fast for predicting solutions of the uncertain models arising in real physical phenomena.