Analytical Solutions of Fuzzy Linear Differential Equations in the Conformable Setting

Abstract

In this paper, we provide the generalization of two predefined concepts under the name fuzzy conformable differential equations. We solve the fuzzy conformable ordinary differential equations under the strongly generalized conformable derivative. For the order $\Psi$, we use two methods. The first technique is to resolve a fuzzy conformable differential equation into two systems of differential equations according to the two types of derivatives. The second method solves fuzzy conformable differential equations of order $\Psi$ by a variation of the constant formula. Moreover, we generalize our results to solve fuzzy conformable ordinary differential equations of a higher order. Further, we provide some examples in each section for the sake of demonstration of our results.

Exact Solutions and Finite Time Stability of Linear Conformable Fractional Systems with Pure Delay

“…The conformable fractional derivative has main advantages compared with other previous definitions. It can, for example, be used to solve the differential equations and systems exactly and numerically easily and efficiently, it satisfies the product rule and quotient rule, it has results similar to known theorems in classical calculus, and applications for conformable differential equations in a variety of fields have been extensively studied, see [2][3][4][5][6][7][8][9][10] and the references therein. On the other hand, in 2003, Khusainov et al [11] represented the solutions of linear delay differential equations by constructing a new concept of a delayed exponential matrix function.…”

On Fuzzy Conformable Double Laplace Transform with Applications to燩artial Differential Equations

“…Recently, Younus et al [22] generalized two predefined concepts under the name fuzzy conformable differential equations, and got the fuzzy conformable ordinary differential equations under the strongly generalized conformable derivative. For the order , they used two methods.…”