Related papers: A note on the fractional logistic equation
In a recent paper, Saxena et al. [1] developed the solutions of three generalized fractional kinetic equations in terms of Mittag-Leffler functions. The object of the present paper is to further derive the solution of further generalized…
In this article, we present weighted norm inequality for a fractional one-sided minimal function. We prove weighted weak and strong type norm inequalities for the one-sided minimal function on $\mathbb{R}.$ We construct two weight classes…
A fractional diffusion equation with advection term is rigorously derived from a kinetic transport model with a linear turning operator, featuring a fat-tailed equilibrium distribution and a small directional bias due to a given vector…
Lie group method provides an efficient tool to solve a differential equation. This paper suggests a fractional partner for fractional partial differential equations using a fractional characteristic method. A space-time fractional diffusion…
In this paper we consider a class of boundary value problems for third order nonlinear functional differential equation. By the reduction of the problem to operator equation we establish the existence and uniqueness of solution and…
We consider fractional diffusion equation with the distributed order Caputo derivative. We prove existence of a weak and regular solution for general uniformly elliptic operator under the assumption that the weight function is only…
We consider a Dirichlet type problem for a nonlinear, nonlocal equation driven by the degenerate fractional p-Laplacian, with a logistic type reaction depending on a positive parameter. In the subdiffusive and equidiffusive cases, we prove…
Our paper introduces a novel method for calculating the inverse $\mathcal{Z}$-transform of rational functions. Unlike some existing approaches that rely on partial fraction expansion and involve dividing by $z$, our method allows for the…
This paper deals with the \emph{integral} version of the Dirichlet homogeneous fractional Laplace equation. For this problem weighted and fractional Sobolev a priori estimates are provided in terms of the H\"older regularity of the data. By…
In this paper, we investigate the well-posedness of weak solutions to the time-fractional Fokker-Planck equation. Its dynamics is governed by anomalous diffusion, and we consider the most general case of space-time dependent forces.…
In this paper the fractional order logistic map in the sense of Caputo's fractional differences is numerically approached. It is shown that the necessary iterations number to avoid transients must be of order of thousand, not of order of…
In this article we study the numerical approximation of a variable coefficient fractional diffusion equation. Using a change of variable, the variable coefficient fractional diffusion equation is transformed into a constant coefficient…
This note presents a few observations on the nonlocal nature of quantum errors and the expected performance of the recently proposed quantum error-correction codes that are based on the assumption that the errors are either bit-flip or…
Nonlinear fractional differential equations have gained a significant place in mathematical physics. Finding the solutions to these equations has emerged as a field of study that has attracted a lot of attention lately. In this work, semi…
The purpose of this note is to present a formulation of a given nonlinear ordinary differential equation into an equivalent system of linear ordinary differential equations. It is evident that the easiness of a such procedure would be able…
This paper aims to investigate a multi-dimensional transport equation with nonlocal velocity and fractional dissipation.The balance between the nonlinearity and dissipation gives rise to three different cases, namely the subcritical,…
Fractional differential equations (FDEs) are an extension of the theory of fractional calculus. However, due to the difficulty in finding analytical solutions, there have not been extensive applications of FDEs until recent decades. With…
In this paper, first a class of fractional differential equations are obtained by using the fractional variational principles. We find a fractional Lagrangian $L(x(t)$, where $_a^cD_t^\alpha x(t))$ and $0<\alpha< 1$, such that the following…
This work proposes a conformable fractional predictor-corrector algorithm for solving conformable fractional differential equations. Fractional calculus is finding applications in various scientific fields, but existing numerical methods…
We derive some regularity estimates of the solution to a time fractional diffusion equation, that are useful for numerical analysis, and partially unravel the singularity structure of the solution with respect to the time variable.