In this study, we explore a recent biological model created to analyze the behavior of cancer cells by administering dose drug containing anti-PD-L1 and IL-10 with Caputo Atangana–Baleanu derivative in sense (ABC). Using order examine stability non-linear system, are able demonstrate that it is existent unique, introduce several numeric data obtained for fractional values MATLAB using Adams–Bas...

In this work we consider the abstract Cauchy problem with Caputo fractional time derivative of order $$\alpha \in (0,1]$$ , and discuss continuity respective solutions regarding parameter $$ . We also present a study about Mittag-Leffler families operators (for ), when they are induced by sectorial operators.

In this article a modification of the Chebyshev collocation method is applied to the solution of space fractional differential equations.The fractional derivative is considered in the Caputo sense.The finite difference scheme and Chebyshev collocation method are used .The numerical results obtained by this way have been compared with other methods.The results show the reliability and efficiency...

In this work, we consider variable order difusion and wave equations. The derivative is describedin the Caputo sence of variable order. We use the Genocchi polynomials as basic functions andobtain operational matrices via these polynomials. These matrices and collocation method help usto convert variable order diusion and wave equations to an algebraic system. Some examples aregiven to show the...

This paper develops appropriate boundary conditions for the two-sided fractional diffusion equation, where the usual second derivative in space is replaced by a weighted average of positive and negative fractional derivatives. Mass preserving, reflecting boundary conditions for two-sided fractional diffusion involve a balance of left and right fractional derivatives at the boundary. Stable, con...

The current study is devoted to investigating the existence and uniqueness of solutions for a new class symmetrically coupled system nonlinear hyperbolic partial-fractional differential equations in generalized Banach spaces sense ψ–Caputo partial fractional derivative. Our approach based on Krasnoselskii-type fixed point theorem Perov’s together with Bielecki norm, while Urs’s was used prove U...

A generalized mathematical model of the breast and ovarian cancer is developed by considering fractional differential equations with Caputo time-fractional derivatives. The use shows that time-evolution proliferating cell mass, quiescent proliferative function are significantly influenced their history. Even if classical model, based on derivative integer order has been studied in many papers, ...

In this work we study integral boundary value problem involving Caputo differentiation  cD tu(t) = f(t, u(t)), 0 < t < 1, αu(0)− βu(1) = ∫ 1 0 h(t)u(t)dt, γu′(0)− δu′(1) = ∫ 1 0 g(t)u(t)dt, where α, β, γ, δ are constants with α > β > 0, γ > δ > 0, f ∈ C([0, 1]×R+,R), g, h ∈ C([0, 1],R+) and cD t is the standard Caputo fractional derivative of fractional order q(1 < q < 2). By using some fix...