Examples of Expansions in Fractional Powers, and Applications

Abstract

We approximate the solution of a generalized form of the Bagley–Torvik equation using Taylor’s expansions in fractional powers. Then, we study the fractional Laguerre-type logistic equation by considering the fractional exponential function and its Laguerre-type form. To verify our findings, we conduct numerical tests using the computer algebra program Mathematica©.

Keywords

• fractional differential equations
• Bagley–Torvik equation
• generalized exponential function
• Mittag–Leffler function
• fractional Laguerre-type logistic equation