*Correspondence: [email protected] 1Department of Mathematical Sciences, UAE University, P.O. Box 15551, Al Ain, UAE Full list of author information is available at the end of the article Abstract In this paper we study linear and nonlinear fractional diffusion equations with the Caputo fractional derivative of non-singular kernel that has been launched recently (Caputo and Fabrizio in Prog....

Abstract In this paper we study fractional initial value problems with Caputo–Fabrizio derivative which involves nonsingular kernel. First apply α - ℓ -contraction and -type F mappings to the existence uniqueness of solutions for such problems. Finally, use some contraction in complete $\mathfrak{F}$ F -metri...

In this paper, a tumor-immune interaction model has been analyzed via Caputo-Fabrizio fractional derivative operator with exponential kernel. Existence of solution the established fixed-point method and then it demonstrated uniqueness also. The stability help Hyers-Ulam approach numerical by using Adam-Basford method. results are further examined in detail simulations for different values.

in this article, we survey the asymptotic stability analysis of fractional differential systems with the prabhakar fractional derivatives. we present the stability regions for these types of fractional differential systems. a brief comparison with the stability aspects of fractional differential systems in the sense of riemann-liouville fractional derivatives is also given.

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...

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 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 < ? 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...