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**1 - 2**of**2**### 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 operator ..."

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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.

### Research Article Solution of Some Types of Differential Equations: Operational Calculus and Inverse Differential Operators

"... Copyright © 2014 K. Zhukovsky.This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. We present a generalmethod of operational nature to ana ..."

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Copyright © 2014 K. Zhukovsky.This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. We present a generalmethod of operational nature to analyze and obtain solutions for a variety of equations ofmathematical physics and related mathematical problems. We construct inverse differential operators and produce operational identities, involving inverse derivatives and families of generalised orthogonal polynomials, such as Hermite and Laguerre polynomial families. We develop the methodology of inverse and exponential operators, employing them for the study of partial differential equations. Advantages of the operational technique, combined with the use of integral transforms, generating functions with exponentials and their integrals, for solving a wide class of partial derivative equations, related to heat, wave, and transport problems, are demonstrated. 1.