Nowadays, fractional derivative is used to model various problems in science and engineering. In this paper, a new numerical method approximate the generalized Hattaf involving nonsingular kernel proposed. This included several forms existing literature such as Caputo–Fabrizio derivative, Atangana–Baleanu weighted derivative. The proposed based on Lagrange polynomial interpolation, it applied s...

In this article, we have investigated the fractional-order Burgers equation via Natural decomposition method with nonsingular kernel derivatives. The two types of fractional derivatives are used in article Caputo–Fabrizio and Atangana–Baleanu derivative. We employed transform on followed by inverse transform, to achieve result equations. To validate method, considered a examples compared exact ...

In this paper, we study a new approach of investigation existence, uniqueness and stability the periodic solution nonlinear fractional integro-differential equation type Caputo-Fabrizio derivative with initial condition, boundary conditions, integral conditions by using successive approximations method Banach fixed point theorem. Finally, some examples are present to illustrate theorems.

the present study aims at indicating the existence and uniqueness result of system in extended colombeaualgebra. the caputo fractional derivative is used for solving the system of odes. in addition, rieszfractional derivative of colombeau generalized algebra is considered. the purpose of introducing rieszfractional derivative is regularizing it in colombeau sense. we also give a solution to a n...

This survey paper is concerned with some of the most recent results on Lyapunov-type inequalities for fractional boundary value problems involving a variety derivative operators and conditions. Our work deals Caputo, Riemann-Liouville, ?-Caputo, ?-Hilfer, hybrid, Caputo-Fabrizio, Hadamard, Katugampola, Hilfer-Katugampola, p-Laplacian, proportional operators.