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...

Stability of the solutions to a nonlinear impulsive Caputo fractional differential equation is studied using Lyapunov like functions. The derivative of piecewise continuous Lyapunov functions among the nonlinear impulsive Caputo differential equation of fractional order is defined. This definition is a natural generalization of the Caputo fractional Dini derivative of a function. Several suffic...

We prove that a free relativistic rotor (or rotator) Klein-Gordon field is massless. To this end, the magnitude of the centrifugal force and its associated quantum operator for a free particle with a circular motion are determined in Special Relativity. A partial differential equation including the centrifugal force operator is derived. Finally, from the conjunction of the above equation and th...

this paper studies the existence of solutions for acoupled system of nonlinear fractional differential equations. newexistence and uniqueness results are established using banach fixedpoint theorem. other existence results are obtained using schaeferand krasnoselskii fixed point theorems. some illustrative examplesare also presented.

Using a density matrix description in space we study the evolution of wavepackets in a fluctuating space–time background. We assume that space–time fluctuations manifest as classical fluctuations of the metric. From the non–relativistic limit of a non-minimally coupled Klein–Gordon equation we derive a Schrödinger equation with an additive gaussian random potential. This is transformed into an ...

many simulation algorithms (chemical reaction systems, differential systems arising from the modeling of transient behavior in the process industries and etc.) contain the numerical solution of systems of differential equations. for the efficient solution of the above mentioned problems, linear multistep methods or runge-kutta technique are used. for the simulation of chemical procedures the ra...