Applying VIM to conformable partial differential equations

In this paper, we used new conformable variational iteration method, by the conformable derivative, for solving fractional heat-like and wave-like equations. This method is simple and very effective in the solution procedures of the fractional partial differential equations that have complicated solutions with classical fractional derivative definitions like Caputo, Riemann-Liouville and etc. The results show that conformable variational iteration method is usable and convenient for the solution of fractional partial differential equations. Obtained results are compared to the exact solutions and their graphics are plotted to demonstrate efficiency and accuracy of the method.Publisher's Versio

Existence, Uniqueness and Approximate Solutions of Fuzzy Fractional Differential Equations

In this paper, the Cauchy problem of fuzzy fractional differential equations Tγut=Ftut, ut0=u0, with fuzzy conformable fractional derivative (γ-differentiability, where γ∈01) are introduced. We study the existence and uniqueness of solutions and approximate solutions for the fuzzy-valued mappings of a real variable, we prove some results by applying the embedding theorem, and the properties of the fuzzy solution are investigated and developed. Also, we show the relation between a solution and its approximate solutions to the fuzzy fractional differential equations of order γ

Study of a Dynamical Problem under Fuzzy Conformable Differential Equation

The notion of inclusion by generalized conformable differentiability is used to analyze fuzzy conformable differential equations (FCDE). This idea is based on expanding the class of conformable differentiable fuzzy mappings, and we use generalized lateral conformable derivatives to do so. We’ll see that both conformable derivatives are distinct and that they lead to different FCDE solutions. The approach’s utility and efficiency are demonstrated with an example

Fuzzy Generalized Conformable Fractional Derivative

We give a new definition of fuzzy fractional derivative called fuzzy conformable fractional derivative. Using this definition, we prove some results and we introduce new definition of generalized fuzzy conformable fractional derivative

Solving Higher-Order Fractional Differential Equations by the Fuzzy Generalized Conformable Derivatives

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