This paper deals with a ratio-dependent functional response predator-prey model with a fractional order derivative. The ratio-dependent models are very interesting, since they expose neither the paradox of enrichment nor the biological control paradox. We study the local stability of equilibria of the original system and its discretized counterpart. We show that the discretized system, which is...

Anomalous diffusion with ballistic scaling is characterized by a linear spreading rate with respect to time that scales like pure advection. Ballistic scaling may be modeled with a symmetric Riesz derivative if the spreading is symmetric. However, ballistic scaling coupled with a skewness is observed in many applications, including hydrology, nuclear physics, viscoelasticity, and acoustics. The...

in this article, we survey the asymptotic stability analysis of fractional differential systems with the prabhakar fractional derivatives. we present the stability regions for these types of fractional differential systems. a brief comparison with the stability aspects of fractional differential systems in the sense of riemann-liouville fractional derivatives is also given.

Navier–Stokes equations (NS-equations) are applied extensively for the study of various waves phenomena where symmetries involved. In this paper, we discuss NS-equations with time-fractional derivative order β∈(0,1). fractional media, these can be utilized to recreate anomalous diffusion which used construct symmetries. We examine initial value problem involving symmetric Stokes operator and gr...

We relate the fractional powers of the discrete Laplacian with a standard time-fractional derivative in the sense of Liouville by encoding the iterative nature of the discrete operator through a time-fractional memory term.

Abstract This paper proposes a local meshless radial basis function (RBF) method to obtain the solution of two-dimensional time-fractional Sobolev equation. The model is formulated with Caputo fractional derivative. uses RBF approximate spatial operator, and finite-difference algorithm as time-stepping approach for in time. stability technique examined by using matrix method. Finally, two numer...

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...

We prove duality between the left and right fractional derivatives, independently on the type of fractional operator. Main result asserts that the right derivative of a function is the dual of the left derivative of the dual function or, equivalently, the left derivative of a function is the dual of the right derivative of the dual function. Such duality between left and right fractional operat...

Abstract. We consider Hadamard fractional derivatives and integrals of variable fractional order. A new type of fractional operator, which we call the Hadamard–Marchaud fractional derivative, is also considered. The objective is to represent these operators as series of terms involving integer-order derivatives only, and then approximate the fractional operators by a finite sum. An upper bound ...