# The Generating Operators of Generalized H-transforms

Chapter

## Abstract

It is well known that the Laplace transform (3.50) possesses the following property
where the function

$$
L\left\{ {\frac{d}
{{dt}}f\left( t \right);x} \right\} = xL\left\{ {f\left( t \right);x} \right\} - f\left( 0 \right),
$$

(1)

*f*(*t*) belongs to a suitable space of functions. This formula is used, for example, for the solution of ordinary differential equations with constant coefficients. We saw that the Laplace transform is a particular case of the*H*-transform. In this chapter, we will obtain the analogue of formula (5.1) for the generalized*H*-transform (4.1), which is reduced under some conditions to the*H*-transform (see the Theorem 4.1). Note that the case of the generalized*G*-transform was considered by Yu. F. Luchko and S.B. Yakubovich (1991) and the results for the generalized*H*-transform can be found in Yu.F. Luchko and S.B. Yakubovich (1991a).## Keywords

Generate Operator Constant Coefficient Fractional Integral Absolute Constant Integral Transform
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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## Copyright information

© Springer Science+Business Media Dordrecht 1994