In this article, the active control method is used for hybrid synchronization between two fractional order hyperchaotic systems, Chen hyperchaotic system taken as the master system and the other fractional order hyperchaoticLu system taken as slave system separately. The fractional derivative is described in Caputo sense. Numerical simulation results which are carried out using Adams–Bashforth–...

In this article, the modified simple equation method has been extended to celebrate the exact solutions of nonlinear partial time-space differential equations of fractional order. Firstly, the fractional complex transformation has been implemented to convert nonlinear partial fractional differential equations into nonlinear ordinary differential equations. Afterwards, modified simple equation m...

As an extension of the fact that a sectorial operator can determine an analytic semigroup, we first show that a sectorial operator can determine a real analytic α-order fractional resolvent which is defined in terms of MittagLeffler function and the curve integral. Then we give some properties of real analytic α-order fractional resolvent. Finally, based on these properties, we discuss the regu...

The primary aim of this manuscript is to present the approximate analytical solutions of the time fractional order α (1<α≤2) Vibration Equation (VE) of large membranes with the use of an iterative technique namely Residual Power Series Method (RPSM). The fractional derivative is defined in the Caputo sense. Example problems have been solved to demonstrate the efficacy of the present method and ...

In this article, a numerical study for the fractional wave equations is introduced by using a class of finite difference methods. These methods are extension of the weighted average methods for ordinary (non-fractional) wave equations. The stability analysis of the proposed methods is given by a recently proposed procedure similar to the standard John von Neumann stability analysis. Simple and ...

The inverse stable subordinator is the first passage time of a standard stable subordinator with index 0 < β < 1. The probability density of the inverse stable subordinator can be used to solve time-fractional Cauchy problems, where the usual first derivative in time is replaced by a Caputo fractional derivative of order β. If the Cauchyproblemgoverns aMarkov process, then the fractional Cauchy...

Anomalous dispersion is observed throughout hydrology, yielding a contaminant plume with heavy leading tails. The fractional advection dispersion equation (FADE) captures this behavior by replacing the second-order spatial derivative with a Riemann-Liouville (RL) fractional derivative. The RL fractional derivative is a nonlocal operator and models large jumps of solute particles in heterogeneou...

‎In this paper we propose a method for computing approximations of solution of fuzzy fractional differential equations using fuzzy variational iteration method. Defining a fuzzy fractional derivative, we verify the utility of the method through two illustrative ‎examples.‎

Lie point symmetries of time-fractional potential Burgers' equation are presented. Using these symmetries fractional potential Burgers' equation has been transformed into an ordinary differential equation of fractional order corresponding to the Erdélyi-Kober fractional derivative. Further, an analytic solution is furnished by means of the invariant subspace method. AMS subject classifications:...