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

Abstract

In this paper, we consider the Prabhakar fractional logistic differential equation. By using appropriate limit relations, we recover some other logistic differential equations, giving representations of each solution in terms of a formal power series. Some numerical approximations are implemented by using truncated series.

Keywords

• logistic differential equation
• fractional calculus
• Liouville–Caputo fractional derivative
• Atangana–Baleanu derivative
• Caputo–Fabrizio derivative
• Prabhakar derivative