Fractional solutions of a general class of non-Fuchsian differential equations

Fractional Analysis has an important place in the scientific world as a remarkable field with its applications in various problems. In recent years, studies in this field have spread not only to fields such as mathematics, physics and engineering, but also to many different disciplines such as biology and economics. In this study, we consider a class of differential equations of the non-Fuchsian type with six parameters, and obtain a second-order differential equation with variable coefficients having singular points with the help of appropriate transformations using uncertain parameters. Then, by reducing the obtained second-order homogeneous and non-homogeneous differential equations to first-order linear differential equations with the help of fractional analysis and fractional calculus operators, their explicit solutions are obtained.