This paper introduces techniques for the estimation of solutions to fractional order differential equations (FODEs) and the approximation of a function’s Caputo fractional derivative. These techniques are based on scattered data interpolation via reproducing kernel Hilbert spaces (RKHSs). Specifically, an RKHS is generated for the purpose of estimating fractional derivatives from the Mittag-Lef...

This article presents the analytical study of three species fractional food web model in framework Modified Caputo–Fabrizio operator. With help fixed point theory, existence and uniqueness results are investigated for order model. To obtain approximate solution suggested model, well-known Laplace–Adomian decomposition method is used. The solutions validated through simulations with a variety or...

The functional effects of medications, such as those that slow down and calm the body, have been investigated for polarized diffusion coefficient based on subsequent increase through magnetism. This study examines generalized Mittag–Lefer kernel-based fractional derivatives in MHD Brinkman-type fluids under bioconvection contain hybrid titanium dioxide (TiO 2 ) silver (Ag) nanoparticles with wa...

In this paper, a modification of variational iteration method is applied to solve fractional integro-differential equations. The fractional derivative is considered in the Caputo sense. Through examples, we will see the modified method performs extremely effective in terms of efficiency and simplicity to solve fractional integro-differential equations. 2000 Mathematics Subject Classification: 6...

and Applied Analysis 3 The left Caputo fractional derivative is C aD f t 1 Γ n − α ∫ t a t − τ n−α−1 ( d dτ )n f τ dτ, 2.6 while the right Caputo fractional derivative is

A fractional calculus concept is considered in the framework of a Volterra type integro-differential equation, which employed for self-consistent description high-gain free-electron laser (FEL). It shown that Fox H-function Laplace image kernel also known as FEL equation with Caputo–Fabrizio derivative. Asymptotic solutions are analyzed well.

Abstract In this work, a coupled system of time-fractional modified Burgers’ equations is considered. Three different fractional operators: Caputo, Caputo-Fabrizio and Atangana-Baleanu operators are implemented for the equations. Also, two scenarios examined each operator: when initial conditions u(x, y, 0) = sin(xy), v(x, they e {−kxy} , where k, α some positive constants. With aid computable ...

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...