Linear canonical transform is an integral transform with four parameters and has been proved to be powerful tool for optics, radar system analysis, filter design etc. Fractional Fourier transform and Fresnel transform can be seen as a special case of linear canonical transform with real parameters. Further generalization of linear canonical transform with complex parameters is also developed an...

this paper presents an analytical model characterizing unsteady groundwater flow in an unconfined aquifer resting on a sloping impervious bed. the aquifer is in contact with a constant water level at one end. the other end is connected to a stream whose level is increasing form an initial level to a final level at a known exponentially decaying function of time. moreover, the aquifer is repleni...

In the present paper the authors introduce the exponential integral transform and the complementary error transform, then it is shown that the third iterate of the Laplace transform is the exponential integral transform and a modified third iterate of the Laplace transform is the complementary error transform. Some identities involving these new transforms, the Laplace transform and the Stieltj...

In this article, we show that Laplace transform can be applied to fractional system. To this end, solutions of linear fractional-order equations are first derived by a direct method, without using Laplace transform. Then the solutions of fractional-order differential equations are estimated by employing Gronwall and Hölder inequalities. They are showed be to of exponential order, which are nece...

For a skip-free Markov process on Z + with generator matrix Q, we evaluate the joint Laplace transform of the occupation times before hitting the state n (starting at 0). This Laplace transform has a very straightforward and familiar expression. We investigate the properties of this Laplace transform, especially the conditions under which the occupation times form a Markov chain.

In this paper we present an extension of Fractional Laplace Transform in the framework non-conformable local fractional derivative. Its main properties are studied and it is applied to resolution differential equations.

In this paper we introduce a generalized Laplace transform in order to work with very general fractional derivative, and obtain the properties of new transform. We also include corresponding convolution inverse formula. particular, definition for improves previous results. Additionally, deal harmonic oscillator equation, showing that its allow one solve differential equations.