Inverse Derivative and Solutions of Some Ordinary Differential Equations

Abstract

We present a general method of operational nature to obtain solutions for several types of differential equations. Methodology of inverse differential operators for the solution of differential equations is developed. We apply operational approach to construct inverse differential operators and develop operational identities, involving inverse derivatives and generalized families of orthogonal polynomials. We employ them together with the exponential operator to investigate various differential equations. Advantages of operational technique for finding solutions of a wide spectrum of differential equations are demonstrated, in particular with regard to fractional differential equations.