Numerical evaluations of Caputo fractional derivatives for scattered noisy data is an important problem in scientific research and practical applications. Fractional derivatives have been applied recently to the numerical solution of problems in fluid and continuum mechanics. The Caputo fractional derivative of order α is given as follows f (t) = 1 Γ(1− α) ∫ t 0 f (s) (t− s)α ds, 0 < α < 1 The ...

and Applied Analysis 3 Definition 2.2 see 18 . The standard Riemann-Liouville fractional derivative of order α > 0 of a continuous function y : a,∞ → R is given by D a y t 1 Γ n − α ( d dt )n ∫ t a t − s n−α−1y s ds, 2.2 where n α 1, provided that the integral on the right-hand side converges. Definition 2.3 see 18 . The Riemann-Liouville fractional integral of order α > 0 of a function y : a,∞...

The unstable equilibrium points of the fractional-order Lorenz chaotic system can be controlled via fractional-order derivative, and chaos synchronization for the fractional-order Lorenz chaotic system can be achieved via fractional-order derivative. The control and synchronization technique, based on stability theory of fractional-order systems, is simple and theoretically rigorous. The numeri...

in this paper, we solve a inhomogeneous fractional klein-gordon equation by the method of separating variables. we apply the method for three boundary conditions, contain dirichlet, neumann, and robin boundary conditions, and solve some examples to illustrate the effectiveness of the method.

The fractional derivatives in the sense of Caputo, and the homotopy analysis method (HAM) are used to construct the approximate solutions for nonlinear fractional dispersive long wave equation with reaspect to time fractional derivative. The HAM contains a certain auxiliary parameter which provides us with a simple way to adjust and control the convergence region and rate of convergence of the ...

Smoking is one of the most common habits in world. Due to harmful substances contained it cigarette disturb people’s health and causes their death. Every year, many people lose from smoking or by direct exposure cigarettes. In this study, we conducted a new application stability analysis related fractional model use. This consists three compartments: potential smokers (P), (S) defi-nitely quitt...

In this paper we investigate existence of solutions for the system: Dtαu=div(u∇p),Dtαp=−(−Δ)sp+u2,in T3 0<s≤1, and 0<α≤1. The term Dtαu denotes Caputo derivative, which models memory effects in time. fractional Laplacian (−Δ)s represents Lévy diffusion. We prove global nonnegative weak that satisfy a variational inequality. proof uses several approximations steps, including an implicit Euler ti...

In this study, we propose a secure communication scheme based on the synchronization of two identical fractional-order chaotic systems. The fractional-order derivative is in Caputo sense, and for synchronization, we use a robust sliding-mode control scheme. The designed sliding surface is taken simply due to using special technic for fractional-order systems. Also, unlike most manuscripts, the ...