The present study aims at indicating the existence and uniqueness result of system in extended colombeau algebra. The Caputo fractional derivative is used for solving the system of ODEs. In addition, Riesz fractional derivative of  Colombeau generalized algebra is considered. The purpose of introducing Riesz fractional derivative is regularizing it in Colombeau sense. We also give a solution to...

In this paper we establish some convergence results for Riemann-Liouville, Caputo, and Caputo-Fabrizio fractional operators when the order of differentiation approaches one. We consider errors given by $\left|\left| D^{1-\al}f -f'\right|\right|_p$ p=1 $p=\infty$ prove that both Caputo Fabrizio is a positive real r, 0<r<1. Finally, compare speed between obtaining they related Digamma function.

A coupled system under Caputo-Fabrizio fractional order derivative (CFFOD) with antiperiodic boundary condition is considered. We use piecewise version of CFFOD. Sufficient conditions for the existence and uniqueness solution by ap?plying Banach, Krasnoselskii?s fixed point theorems. Also some appropriate results Hyers-Ulam (H-U) stability analysis established. Proper example given to verify re...

In this study we have proposed the SIAQR model with time-dependent infection rate. The model’s well-posedness is demonstrated, and then extended to fractional mathematical by employing Caputo-Fabrizio derivative operator. We also used Lipschitz condition linear growth determine conditions under which has a unique solution. numerical solutions are presented. Furthermore, using graphical represen...

In this paper, using Caputo-Fabrizio fractional derivative, we obtain some new results for the existence and uniqueness of solutions differential equation with nonlocal initial value about order 0 &lt; ? 1 . These are applied help Arzela-Ascoli theorem Schauder fixed point. Also based on ?-contractive maps such problems, unique has been introduced proved. Finally, illustrative example is consid...

In this paper, we propose a high-precision discrete scheme for the time-fractional diffusion equation (TFDE) with Caputo-Fabrizio type. First, special of C-F derivative is used in time direction and compact difference operator space direction. Second, discuss convergence proposed method L 1 ...

A reaction-diffusion system can be represented by the Gray-Scott model. In this study, we discuss a one-dimensional time-fractional model with Liouville-Caputo, Caputo-Fabrizio-Caputo, and Atangana-Baleanu-Caputo fractional derivatives. We utilize homotopy analysis transformation method to obtain approximate solutions for This gives more realistic series of that converge rapidly exact solution....

in this paper we introduce a type of fractional-order polynomials basedon the classical chebyshev polynomials of the second kind (fcss). also we construct the operationalmatrix of fractional derivative of order $ gamma $ in the caputo for fcss and show that this matrix with the tau method are utilized to reduce the solution of some fractional-order differential equations.

Visceral leishmaniosis is one recent example of a global illness that demands our best efforts at understanding. Thus, mathematical modeling may be utilized to learn more about and make better epidemic forecasts. By taking into account the Caputo Caputo-Fabrizio derivatives, frictional model visceral was mathematically examined based on real data from Gedaref State, Sudan. The stability analysi...