Fractional differential equations involving Erdélyi–Kober derivatives with variable coefficients

Abstract

We consider multi-term fractional differential equations with continuous variable coefficients and differential operators of Erdélyi–Kober type and multiple independent fractional orders. We solve such equations in a general framework, obtaining explicit solutions in the form of uniformly convergent series. By considering several particular cases, we verify the consistency of our results with others previously obtained in the literature.