Abstract
In this paper, the generalized concept of conformable fractional derivatives of order q ∈ n , n + 1 for fuzzy functions is introduced. We presented the definition and proved properties and theorems of these derivatives. The fuzzy conformable fractional differential equations and the properties of the fuzzy solution are investigated, developed, and proved. Some examples are provided for both the new solutions.
Highlights
A closed-form solution for nonlinear fractional differential equations (FDEs) plays a significant role in understanding the qualitative as well as quantitative features of complex physical phenomena. e nonlinear FDEs appear in different sciences and engineering problems such as control theory, signal processing, finance, electricity, mechanics, plasma physics, stochastic dynamical system, economics, and electrochemistry [1,2,3,4,5,6,7]
Our objective of this article is to present a generalized concept of conformable fractional derivative of order q ∈
F is q(n,m)-differentiable on I, if D1n exists on I and it is p(m)-differentiable on I and p(m) q(n,m) − 1. e q-differentiable (conformable fractional derivatives of order q ∈ (0, 1]) of F is denoted by Tq(n,m)F(t) for n, m 1, 2
Summary
A closed-form solution for nonlinear fractional differential equations (FDEs) plays a significant role in understanding the qualitative as well as quantitative features of complex physical phenomena. e nonlinear FDEs appear in different sciences and engineering problems such as control theory, signal processing, finance, electricity, mechanics, plasma physics, stochastic dynamical system, economics, and electrochemistry [1,2,3,4,5,6,7]. A closed-form solution for nonlinear fractional differential equations (FDEs) plays a significant role in understanding the qualitative as well as quantitative features of complex physical phenomena. Khalid et al [11] introduced a new simple definition of the fractional derivative named the conformable fractional derivative, which can redress shortcomings of the other definitions, and this new definition satisfies formulas of derivative of product and quotient of two functions [12, 13]. Harir et al [14] introduced the fuzzy generalized conformable fractional derivative, which generalized and extended the concept of Hukuhara differentiability for set-valued mappings to the class of fuzzy mapping [15, 16]. Our objective of this article is to present a generalized concept of conformable fractional derivative of order q ∈ We interpret fuzzy conformable fractional differential equations using this concept.
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