Fractional Quasi-Bessel Equations

TL;DR

This paper develops a theory for fractional quasi-Bessel equations, establishing existence and uniqueness of solutions within fractional series, and extends results to various fractional differential equations.

Contribution

It introduces a new framework for analyzing fractional quasi-Bessel equations, broadening the understanding of fractional differential equations including Cauchy-Euler types.

Findings

Established existence and uniqueness in fractional series

Extended results to Cauchy-Euler and constant-coefficient equations

Provided a new methodological approach for fractional differential equations

Abstract

In this paper we consider fractional quasi-Bessel equations $$\sum_{i=1}^{m}d_i x^{\alpha_i+p_i}D^{\alpha_i} u(x) + (x^\beta - \nu^2)u(x)=0$$ and construct their existence and uniqueness theory in the class of fractional series. Our methodology allows us to obtain new results for a broad class of fractional differential equations including Cauchy-Euler and constant-coefficient equations.