The paper presents an adaptation of numerical solution of first order linear differential equation in fuzzy environment. The numerical method is re-established and studied with fuzzy concept to estimate its uncertain parameters whose values are not precisely known. Demonstrations of fuzzy solutions of the governing methods are carried out by the approaches, namely Modified Runge Kutta method an...

This paper studies a new class of instantaneous and non-instantaneous impulsive boundary value problem involving the generalized ?-Caputo fractional derivative with weight. Depending on critical point theorems some properties ?-Caputo-type integration differentiation, variational construction multiplicity result solutions are established.

A new time-fractional derivative with Mittag-Leffler memory kernel, called the generalized Atangana-Baleanu is defined along associated integral operator. Some properties of operators are proved. The operator suitable to generate by particularization known Atangana-Baleanu, Caputo-Fabrizio and Caputo derivatives. mathematical model advection-dispersion process kinetic adsorption formulated cons...

and Applied Analysis 3 The left Caputo fractional derivative is C aD f t 1 Γ n − α ∫ t a t − τ n−α−1 ( d dτ )n f τ dτ, 2.6 while the right Caputo fractional derivative is

and Applied Analysis 3 Let Γ(⋅) denote the gamma function. For any positive integer n and real number θ (n − 1 < θ < n), there are different definitions of fractional derivatives with order θ in [8]. During this paper, we consider the left, (right) Caputo derivative and left (right) Riemann-Liouville derivative defined as follows: (i) the left Caputo derivative: C 0 D θ t V (t) = 1 Γ (n − θ) ∫ ...

In this paper the substantiation of the method of full averaging for fuzzy differential inclusions is considered. These results generalize the results of [17, 20] for differential inclusions with Hukuhara derivative and of [18] for fuzzy differential equations.

Abstract: In this paper, we studied the numerical solution of a time-fractional Korteweg–de Vries (KdV) equation with new generalized fractional derivative proposed recently. The fractional derivative employed in this paper was defined in Caputo sense and contained a scale function and a weight function. A finite difference/collocation scheme based on Jacobi–Gauss–Lobatto (JGL) nodes was applie...

The main focus of this paper is to develop an efficient analytical method obtain the traveling wave fuzzy solution for generalized Hukuhara conformable fractional equations by considering type differentiability solution. To achieve this, derivative based on defined, and several properties are brought topic, such as switching points chain rule. After that, a new applied find exact solutions two ...