Related papers: A note on the fractional logistic equation

As is well known, the idea of a fractional sum and difference on uniform lattice is more current, and gets a lot of development in this field. But the definitions of fractional sum and fractional difference of $f(z)$ on non-uniform lattices…

The logistic equation is often considered as a simplification of the chemostat (Kooi, Boer, Kooijman (1998)). However, the global qualitative properties of the delayed single species chemostat are completely known, see e. g. Smith (2011).…

This manuscript studies the numerical solution of the time-fractional Burgers-Huxley equation in a reproducing kernel Hilbert space. The analytical solution of the equation is obtained in terms of a convergent series with easily computable…

We give a new proof of an approximate functional equation, due to J. R. Wilton, for a trigonometric sum involving the divisor function. This allows us to improve on Wilton's error term and to give an explicit formula for an unspecified…

In this paper, we introduce a new method for calculating fractional integrals and differentials. The method involves an equation that we have obtained from infinite applied integration by parts. The equation works for special class of…

To obtain new types of exact travelling wave solutions to nonlinear partial differential equations, a number of approximate methods are known in the literature. In this study, we extend the class of auxiliary equations of Fibonnacci&Lucas…

We show in this comment that the results obtained in a recent work by Yi et al. [Phys. Rev. Lett. 92, 150406 (2004)] are quantitatively not correct and the proposed subsystem Berry phase is not well-defined.

In this paper the generalisation of previous author's formulation of fractional continuum mechanics to the case of anisotropic non-locality is presented. The considerations include the review of competitive formulations available in…

We present a new numerical tool to solve partial differential equations involving Caputo derivatives of fractional variable order. Three Caputo-type fractional operators are considered, and for each one of them an approximation formula is…

Numerical solving differential equations with fractional derivatives requires elimination of the singularity which is inherent in the standard definition of fractional derivatives. The method of integration by parts to eliminate this…

We prove a useful formula and new properties for the recently introduced power fractional calculus with non-local and non-singular kernels. In particular, we prove a new version of Gronwall's inequality involving the power fractional…

We study a nonlinear stochastic partial differential equation whose solution is the conditional log-Laplace functional of a superprocess in a random environment. We establish its existence and uniqueness by smoothing out the nonlinear term…

In this work we wish to highlight some consequences of a recent result proved in [N. D. Cong and H. T. Tuan, Generation of nonlocal fractional dynamical systems by fractional differential equations, J. Integral Equations Appl. 29 (2017),…

Conventional finite-difference schemes for solving partial differential equations are based on approximating derivatives by finite-differences. In this work, an alternative theory is proposed which view finite-difference schemes as…

The purpose of this note is to provide a summary of the recent work of the authors on two variations of the pointwise convergence problem for the solutions to the fractional Schr\"odinger equations; convergence along a tangential line and…

We review recent progress in the fractional Calder\'on problem, where one tries to determine an unknown coefficient in a fractional Schr\"odinger equation from exterior measurements of solutions. This equation enjoys remarkable uniqueness…

We prove a global fractional differentiability result via the fractional Caccioppoli-type estimate for solutions to nonlinear elliptic problems with measure data. This work is in fact inspired by the recent paper [B. Avelin, T. Kuusi, G.…

This paper is concerned with an alternative analytical solution of time-fractional nonlinear Schrodinger equation and nonlinear coupled Schrodinger equation obtained by employing fractional reduced differential transform method. The…

The purpose of this paper is to indicate that the recently proposed Momentum fractional least mean squares (mFLMS) algorithm has some serious flaws in its design and analysis. Our apprehensions are based on the evidence we found in the…

Logistic equations play a pivotal role in the study of any non linear evolution process exhibiting growth and saturation. The interest for the phenomenology, they rule, goes well beyond physical processes and cover many aspects of ecology,…