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

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.

The unsteady hydro-magnetic free convection flow with heat transfer of a linearly viscous, incompressible, electrically conducting fluid near a moving vertical plate with the constant heat is investigated. The flow domain is the porous half-space and a magnetic field of a variable direction is applied. The Caputo time-fractional derivative is employed in order to introduce a thermal flux consti...

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...

Physical phenomena and natural disasters, such as tsunamis floods, are caused due to dispersive water waves shallow by earthquakes. In order analyze minimize damaging effects of situations, mathematical models presented different researchers. The Wu–Zhang (WZ) system is one model that describes long waves. this regard, the current study focuses on a non-linear (2 + 1)-dimensional time-fractiona...

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...