In this paper, the long-time behavior of Cesaro mean fundamental solution for fractional Heat equation corresponding to random time changes in Brownian motion is studied. We consider both stable subordinators leading equations with Caputo-Djrbashian derivative and more general cases differential-convolution operators, particular, distributed order derivatives.

We study the uncoupled space-time fractional operators involving time-dependent coefficients and formulate corresponding inverse problems. Our goal is to determine variable from exterior partial measurements of Dirichlet-to-Neumann map. exploit integration by parts formula for Riemann-Liouville Caputo derivatives derive Runge approximation property our operator based on unique continuation Lapl...

Abstract We consider an optimal control problem for a time-dependent obstacle variational inequality involving fractional Liouville–Caputo derivative. The is considered as the control, and corresponding solution to regarded state. Our aim find with properties that state closed given target profile not excessively large in terms of its norm. prove existence results establish necessary conditions...

We give a new method for numerically solving Abel integral equations of first kind. An estimation for the error is obtained. The method is based on approximations of fractional integrals and Caputo derivatives. Using trapezoidal rule and Computer Algebra System Maple, the exact and approximation values of three Abel integral equations are found, illustrating the effectiveness of the proposed ap...

Fractional calculus has been used to model the physical and engineering processes that have found to be best described by fractional differential equations. For that reason, we need a reliable and efficient technique for the solution of fractional differential equations. The aim of this paper is to present an analytical approximation solution for linear and nonlinear multi-order fractional diff...

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 ...

In this article, the variational homotopy perturbation method (VHPM) [proposed in A. Noor et al., Mathematical Problems in Engineering, 1155(10) (2008), 696734] is adopted for solving linear fractional partial differential equations. The aim of this letter is to present an efficient and reliable treatment of the VHPM for the linear fractional partial differential equations. The fractional deriv...

*Correspondence: [email protected] Department of Science, Huaihai Institute of Technology, Cangwu Road, Lianyungang, 222005, China Abstract We apply the Chebyshev polynomial-based differential quadrature method to the solution of a fractional-order Riccati differential equation. The fractional derivative is described in the Caputo sense. We derive and utilize explicit expressions of weighting coef...