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 paper, a new numerical method for solving fractional optimal control problems (focps) is presented. the fractional derivative in the dynamic system is described in the caputo sense. the method is based upon biorthogonal cubic hermite spline multiwavelets approxima-tions. the properties of biorthogonal multiwavelets are first given. the operational matrix of fractional riemann-lioville i...

In this paper, a time fractional diffusion equation on a finite domain is con- sidered. The time fractional diffusion equation is obtained from the standard diffusion equation by replacing the first order time derivative by a fractional derivative of order 0 < a< 1 (in the Riemann-Liovill or Caputo sence). In equation that we consider the time fractional derivative is in...

Stability of the solutions to a nonlinear impulsive Caputo fractional differential equation is studied using Lyapunov like functions. The derivative of piecewise continuous Lyapunov functions among the nonlinear impulsive Caputo differential equation of fractional order is defined. This definition is a natural generalization of the Caputo fractional Dini derivative of a function. Several suffic...

This paper presents a new predictor–corrector numerical scheme suitable for fractional differential equations. An improved explicit Atangana–Seda formula is obtained by considering the neglected terms and used as predictor stage of proposed method. Numerical formulas are presented that approximate classical first derivative well Caputo, Caputo–Fabrizio Atangana–Baleanu derivatives. Simulation r...

This paper establishes some closed formulas for RiemannLiouville impulsive fractional integral calculus and also for RiemannLiouville and Caputo impulsive fractional derivatives. Keywords—RimannLiouville fractional calculus, Caputo fractional derivative, Dirac delta, Distributional derivatives, Highorder distributional derivatives.

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...

In this manuscript, we are interested in the existence result of solution hybrid nonlinear differential equations. involving fractional Caputo Fabrizio derivatives arbitrary order ? ?]0, 1[. By applying Dhage?s fixed point theorem and some analysis techniques, prove our main result. As an application, A non-trivial example is given to demonstrate effectiveness theoretical