Related papers: Fractional Logistic Map

In this short note, we show that the real function recently proposed by Bruce J. West [Exact solution to fractional logistic equation, Physica A 429 (2015) 103--108] is not an exact solution for the fractional logistic equation.

It is pointed out that, for the fractional Fokker-Planck equation for subdiffusion proposed by Metzler, Barkai, and Klafter [Phys. Rev. Lett. 82 (1999) 3563], there are four types of infinitely many exact solutions associated with the newly…

In this work at first the relation the Mittag-Lefler function to the exponential is given. The results are applied to the construction of the solution of Cauchy problem for ordinary linear operator differential equations with constant…

Fractional calculus represents a natural tool for describing relativistic phenomena in pseudo-Euclidean space-time. In this study, Fractional modified special relativity is presented. We obtain fractional generalized relation for the time…

This paper builds on the notion of the so-called orthogonal derivative, where an n-th order derivative is approximated by an integral involving an orthogonal polynomial of degree n. This notion was reviewed in great detail in a paper in J.…

Finite differences, as a subclass of direct methods in the calculus of variations, consist in discretizing the objective functional using appropriate approximations for derivatives that appear in the problem. This article generalizes the…

In the following document, we present a way to obtain the order of convergence of the Fractional Newton-Raphson (F N-R) method, which seems to have an order of convergence at least linearly for the case in which the order $\alpha$ of the…

In this article, some logistic models in the settings of Caputo fractional operators with multi-parametered Mittag-Leffer kernels (ABC) are studied. This study mainly focuses on modified quadratic and cubic logistic models in the presence…

In this paper, we reformulate certain nabla fractional difference equations which had been investigated by other researchers. The previous results seem to be incomplete. By using Contraction Mapping Theorem, we establish conditions under…

In view of the role of reaction equations in physical problems, the authors derive the explicit solution of a fractional reaction equation of general character, that unifies and extends earlier results. Further, an alternative shorter…

Solution of fractional differential equations is an emerging area of present day research because such equations arise in various applied fields. In this paper we have developed analytical method to solve the system of fractional…

An elementary system leading to the notions of fractional integrals and derivatives is considered. Various physical situations whose description is associated with fractional differential equations of motion are discussed.

We introduce a new factorial function which agrees with the usual Euler gamma function at both the positive integers and at all half-integers, but which is also entire. We describe the basic features of this function.

In this note we show how a initial value problem for a relaxation process governed by a differential equation of non-integer order with a constant coefficient may be equivalent to that of a differential equation of the first order with a…

In the present paper we propose a new approach to investigate the logistic function, commonly used in mathematical models in economics and management. The approach is based on indicating in a given time series, having a logistic trend, some…

Recently, Lobb and Nijhoff initiated the study of variational (Lagrangian) structure of discrete integrable systems from the perspective of multi-dimensional consistency. In the present work, we follow this line of research and develop a…

In this paper we construct a new difference analog of the Caputo fractional derivative (called the $L2$-$1_\sigma$ formula). The basic properties of this difference operator are investigated and on its basis some difference schemes…

In this paper we introduce a new mathematical tool to solve fractional equations representing models of fractional systems : The Ultradistributions. Ultradistributions permit us to unify the notion of integral and derivative in one only…

Derivatives of fractional order with respect to time describe long-term memory effects. Using nonlinear differential equation with Caputo fractional derivative of arbitrary order $\alpha>0$, we obtain discrete maps with power-law memory.…

This paper focuses on the fractional difference of Lyapunov functions related to Riemann-Liouville, Caputo and Grunwald-Letnikov definitions. A new way of building Lyapunov functions is introduced and then five inequalities are derived for…