approximating the solution of differential equations of fractional order is necessary because fractional differential equations have extensively been used in physics, chemistry as well as engineering fields. in this paper with central difference approximation and newton cots integration formula, we have found approximate solution for a class of boundary value problems of fractional order. three...

This work explores Kink soliton solution, periodic and rational function solutions for the fractional generalized anti-cubic (FGAC) nonlinearity in fiber Bragg gratings (BGs). The ((D_ζ^α G)/G)-expansion method is employed conjunction with idea of a conformable derivative. Due to its nature, solution looks have some restrictions.

In this paper, we deal with the Duhamel formula, existence, uniqueness, and stability of mild solutions a class nonlocal impulsive differential equations conformable fractional derivative. The main results are based on semigroup theory combined some fixed point theorems. We also give an example to illustrate applicability our abstract results.

In this paper, we introduce the non-conformable double Laplace transform. Its properties are studied, and it is applied to solve some fractional PDEs involving nonconformable derivative. Graphical representations of obtained solutions shown in figures. The study shows that transform effective easy apply create an exact solution for types PDEs.

In this paper, the controllability of differential systems with general conformable derivative is studied. By elaborating rank criterion and Gram criterion, sufficient necessary conditions to investigate that a linear system null completely controllable are given. We obtain full generalization fractional-order case. addition, Krasnoselskii’s fixed point theorem complete result for semilinear ap...

in this article, we survey the asymptotic stability analysis of fractional differential systems with the prabhakar fractional derivatives. we present the stability regions for these types of fractional differential systems. a brief comparison with the stability aspects of fractional differential systems in the sense of riemann-liouville fractional derivatives is also given.