Explicit solutions of Chebyshev equations by fractional differintegral

Fractional analysis which is a branch of mathematical analysis is an extension of the derivative and integral to non-integer (arbitrary) order. It has a wide application area in science and engineering. Our aim is to obtain different solutions for some singular coefficient equations with the aid of fractional analysis and to gain it to literature. In this thesis, it is mentioned that certain solutions of given homogeneous fractional differintegral equations are obtained and these solutions provide the equations. Then, different explicit solutions of the homogeneous and nonhomogeneous Chebyshev equation with singular coefficients were obtained with the aid of definition, theorems and properties of fractional analysis and Leibniz's rule. In addition, the hypergeometric representation, which is another representation of the explicit solutions of the homogeneous Chebyshev equation was found with the help of properties for gamma function and Leibniz's rule.