Solution to the fractional equation with left-sided fractional Bessel derivatives of Gerasimov-Caputo type

TL;DR

This paper introduces a method for solving differential equations involving left-sided fractional Bessel derivatives of Gerasimov-Caputo type, providing explicit solutions using the Meijer integral transform.

Contribution

It presents a novel approach to solving fractional Bessel differential equations with explicit solutions derived via the Meijer transform.

Findings

Explicit solutions for fractional Bessel equations are obtained.

The method extends the applicability of fractional calculus to Bessel-type operators.

The approach facilitates solving similar fractional differential equations on semi-axes.

Abstract

In the article we propose and study a method to solve ordinary differential equations with left-sided fractional Bessel derivatives on semi-axes of Gerasimov-Caputo type. We derive explicit solutions to equations with fractional powers of Bessel operator using the Meijer integral transform.