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 ...

The equivalent system for a multiple-rational-order (MRO) fractional differential system is studied, where the fractional derivative is in the sense of Caputo or Riemann-Liouville. With the relationship between the Caputo derivative and the generalized fractional derivative, we can change the MRO fractional differential system with a Caputo derivative into a higher-dimensional system with the s...

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...

Abstract Our aim in this article is to solve the composite fractional relaxation differential equation by using different definitions of non-integer order derivative operator $D_{t}^{\alpha }$ D t ? , more specifically we employ Caputo, Caputo–Fab...

In the current research work, fractional version of logistic differential model is studied with Allee effect which includes a threshold population. It also initial conditions. The definition derivative utilised in this Caputo-Fabrizio. order to give solution posed problem by an implicit representation, method based on properties used.

In this paper, we study the effect of non-local derivative on Bose-Einstein condensation. Firstly, consider Caputo-Fabrizio fractional order α to derive eigenvalues Schrödinger equation for a free particle in 3D box. Afterwards, condensation an ideal gas with obtained energy spectrum. Interestingly, approach critical temperatures Tc 1 < 2 are greater than standard one. Furthermore, 2D is sho...

In this paper, fractional differential equations in the sense of Caputo-Fabrizio derivative are transformed into integral equations. Then a high order numerical method for equation is investigated by approximating integrand with piece-wise quadratic interpolant. The scheme capable handling both linear and nonlinear A detailed error analysis stability region rigorously established.