Numerical Simulation of Conformable Fuzzy Differential Equations

Abstract

The analytical behavior of differential equations under uncertainty often seems confusing and cannot be fully understood or predicted. Therefore, finding suitable, comprehensive and highly efficient tools to address these issues is of great importance. In this study, an efficient analytical tool is developed to investigate the approximate solution of a class of fuzzy differential equations subject to uncertain initial conditions in the sense of conformable fuzzy fractional derivatives. The proposed technique relies on Taylor series expansion as well as minimizing residual-error function. The methodology is based on constructing a fractional power series in a rapid-convergent form under strongly generalized differentiability without any restrictive assumptions. Parametric characterizing of the solutions is obtained by converting the conformable fuzzy fractional differential equation to an equivalent crisp system of corresponding conformable fractional differential equations. This adaptive can be used as an alternative technique for solving many uncertain problems arising in diverse fields of engineering, chemistry, and biology. The effectiveness, validity, and potentiality of the proposed method are illustrated by verifying a numerical experiment. Numerical and graphical consequences indicate the accuracy and appropriateness of the suggested algorithm in dealing with fuzzy fractional models.