In this paper, we derive a novel numerical method to find out the numerical solution of fractional partial differential equations (PDEs) involving Caputo-Fabrizio (C-F) fractional derivatives. We first find out the approximation formula of C-F derivative of function tk. We approximate the C-F derivative in time with the help of the Legendre spectral method and approximation formula o...

in this paper, first a new homotopy perturbation method for solving a fractional order nonlinear telegraph equation is introduced. by applying the proposed method, the nonlinear equation is translated to linear equations for per iteration of homotopy perturbation method. then, the obtained problems are solved with separation method. in the examples, it is illustrated that the exact solution is ...

A new time-fractional derivative with Mittag-Leffler memory kernel, called the generalized Atangana-Baleanu is defined along associated integral operator. Some properties of operators are proved. The operator suitable to generate by particularization known Atangana-Baleanu, Caputo-Fabrizio and Caputo derivatives. mathematical model advection-dispersion process kinetic adsorption formulated cons...

and Applied Analysis 3 The rest of this paper is organized as follows. In Section 2, preliminaries and problem statement are given. In Section 3, the consensus conditions are derived by using linear matrix inequality approach and matrix’s singular value decomposition. In Section 4, a simulation example is provided to show the advantages of the obtained results. Conclusions are presented in Sect...

in this paper, we present a fractional mathematical model of a one-dimensional phase phase change problem (stefan problem) with latent heat a power function of position. this model includes space-time fractional derivatives in caputo sense and time dependent surface heat flux. an approximate solution of this model is obtained by optimal homotopy asymptotic method (oham) to find an approximate s...

In this paper, we study periodic boundary value problems for a class of linear fractional evolution equations involving the Caputo fractional derivative. Utilizing compactness of the constructed evolution operators and Fredholm alternative theorem, some interesting alternative results for the mild solutions are presented. Periodic motion controllers that are robust to parameter drift are also d...

Szabo's models of acoustic attenuation [Szabo, J. Acoust. Soc. Am. 96(1), 491-500 (1994)] comply well with the empirical frequency power law involving noninteger and odd-integer exponent coefficients while guaranteeing causality, but nevertheless encounter the troublesome issues of hypersingular improper integral and obscurity in implementing initial conditions. The purpose of this paper is to ...

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 ...

This paper deals with the investigation of the solution of an unified fractional reaction-diffusion equation associated with the Caputo derivative as the time-derivative and Riesz-Feller fractional derivative as the space-derivative. The solution is derived by the application of the Laplace and Fourier transforms in closed form in terms of the H-function. The results derived are of general natu...