Fractional Euler numbers and generalized proportional fractional logistic differential equation

Article Mathematics, Applied

Solution of a fractional logistic ordinary differential equation

Juan J. Nieto

Summary: We studied the logistic differential equation of fractional order and non-singular kernel, and obtained the analytical solution.

APPLIED MATHEMATICS LETTERS (2022)

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Article Mathematics, Interdisciplinary Applications

Stability of Generalized Proportional Caputo Fractional Differential Equations by Lyapunov Functions

Ravi Agarwal et al.

Summary: In this paper, stability properties of nonlinear nonautonomous equations with the generalized proportional Caputo fractional derivative (GPFD) are investigated using Lyapunov functions and their GPFDs. A scalar nonlinear fractional differential equation with the GPFD is considered for comparison, and comparison results are proven. Sufficient conditions for stability and asymptotic stability are obtained.

FRACTAL AND FRACTIONAL (2022)

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Article Physics, Multidisciplinary

Power series solution of the fractional logistic equation

I Area et al.

Summary: By using a series of fractional powers, a representation of the solution to the fractional logistic equation is presented and proven to be the exact solution in the simplest case. Numerical approximations demonstrate the good approximations obtained by truncating the fractional power series.

PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS (2021)

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Article Mathematics, Applied

Asymptotic profiles in diffusive logistic equations

Jian-Wen Sun

Summary: This paper focuses on the asymptotic profiles of positive solutions for diffusive logistic equations, particularly examining the sharp effect of nonlinear diffusion functions. By studying both the classical reaction-diffusion equation and nonlocal dispersal equation, the research reveals the distinct roles the nonlinear term plays in evolution problems and stationary solution problems. The sharp changes in the reaction-diffusion equation are proven through regularity estimates and the compact principle, while for nonlocal problems, these changes are obtained through nonlocal estimates and comparison arguments due to the lack of compactness and regularity theory.

ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK (2021)

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Article Mathematics, Interdisciplinary Applications

Fractional-Order Logistic Differential Equation with Mittag-Leffler-Type Kernel

Ivan Area et al.

Summary: In this paper, the Prabhakar fractional logistic differential equation is considered and other logistic differential equations are recovered using appropriate limit relations, with solutions represented in terms of a formal power series. Numerical approximations are implemented using truncated series.

FRACTAL AND FRACTIONAL (2021)

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Article Physics, Multidisciplinary