In this paper, based on the fractional Riccati equation, we propose an extended fractional Riccati sub-equation method for solving fractional partial differential equations. The fractional derivative is defined in the sense of the modified Riemann-Liouville derivative. By a proposed variable transformation, certain fractional partial differential equations are turned into fractional ordinary di...

In this paper, we introduce a generalized composite fading distribution (termed extended generalizedK (EGK)) to model the envelope and the power of the received signal in millimeter wave (60 GHz or above) and free-space optical channels. We obtain the first and the second-order statistics of the received signal envelope characterized by the EGK composite fading distribution. In particular, expr...

The fractional inverse M (real γ > 0) of a matrix M is expanded in a series of Gegenbauer polynomials. If the spectrum of M is confined to an ellipse not including the origin, convergence is exponential, with the same rate as for Chebyshev inversion. The approximants can be improved recursively and lead to an iterative solver for Mx = b in Krylov space. In case of γ = 1/2, the expansion is in t...

In this paper we will present some alternative types of mathematical description and methods of solution of the fractional-order dynamical system in the state space. We point out the difference in the true sense of the name „state“ space for the integer-order and fractional-order system and the importance of the initialization function for the fractionalorder system. Some implications concernin...

Evolution equations for anomalous diffusion employ fractional derivatives in space and time. Linkage between the space-time variables leads to a new type of fractional derivative operator. This paper develops the mathematical foundations of those operators.

Conformable space-time fractional linear telegraph equations are examined using a new method known as conformable Elzaki decomposition method. The suggested combines the Adomian with transform. It is found that numerical simulations confirm effectiveness and reliability of proposed

Fractional order diffusion equations are generalizations of classical diffusion equations which are used to model in physics, finance, engineering, etc. In this paper we present an implicit difference approximation by using the alternating directions implicit (ADI) approach to solve the two-dimensional space-time fractional diffusion equation (2DSTFDE) on a finite domain. Consistency, unconditi...

Abstract. In this work, it has been shown that the combined use of exponential operators and integral transforms provides a powerful tool to solve time fractional generalized KdV of order 2q+1 and certain fractional PDEs. It is shown that exponential operators are an effective method for solving certain fractional linear equations with non-constant coefficients. It may be concluded that the com...

Let L be a positive definite self-adjoint operator on the L2-space associated to a σ-finite measure space. Let H be the dual space of the domain of L1/2 w.r.t. L2(μ). By using an Itô type inequality for the H-norm and an integrability condition for the hyperbound of the semigroup Pt := e −Lt, general extinction results are derived for a class of continuous adapted processes on H. Main applicati...

Abstract Fractional Brownian motion and the fractional Langevin equation are models of anomalous diffusion processes characterized by long-range power-law correlations in time. We employ large-scale computer simulations to study these two geometries, (i) spreading particles on a semi-infinite domain with an absorbing wall at one end (ii) stationary state finite interval boundaries both ends sou...