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, 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.

A fractional calculus concept is considered in the framework of a Volterra type integro-differential equation, which employed for self-consistent description high-gain free-electron laser (FEL). It shown that Fox H-function Laplace image kernel also known as FEL equation with Caputo–Fabrizio derivative. Asymptotic solutions are analyzed well.

In this study, numerical results of a fractional-order multi-dimensional model the Navier–Stokes equations will be achieved via adoption two analytical methods, i.e., Adomian decomposition transform method and q-Homotopy analysis method. The Caputo–Fabrizio operator used to define fractional derivative. proposed methods implemented provide series form given models. techniques validated with exa...

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...