Fractional Euler numbers and generalized proportional fractional logistic differential equation,Fractional Calculus and Applied Analysis

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Fractional Euler numbers and generalized proportional fractional logistic differential equation
Fractional Calculus and Applied Analysis ( IF 2.5 ) Pub Date : 2022-05-27 , DOI: 10.1007/s13540-022-00044-0
Juan J Nieto ₁

Affiliation

We solve a logistic differential equation for generalized proportional Caputo fractional derivative. The solution is found as a fractional power series. The coefficients of that power series are related to the Euler polynomials and Euler numbers as well as to the sequence of Euler’s fractional numbers recently introduced. Some numerical approximations are presented to show the good approximations obtained by truncating the fractional power series. This generalizes previous cases including the Caputo fractional logistic differential equation and Euler’s numbers.

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