Abstract I seems to be widely believed that the Fourier and Laplace transforms are simply related to each other. Nothing could be further from the truth. The Fourier transform is the basis for the Hilbert vector-space expansion of signals. The Laplace transform is the basis of system functions, that are causal. The Fourier transform does not naturally include the step function, which must be sh...

We explore the possibility of using the method of classical integral transforms to solve a class of q-difference-differential equations. The Laplace and the Mellin transform of q-derivatives are derived. The results show that the Mellin transform of the qderivative resembles most closely the corresponding expression in classical analysis, and it could therefore be useful in solving certain q-di...

In this paper, a new mathematical model of a Kelvin-Voigt type thermo-visco-elastic, infinite thermally conducting medium has been considered in the context of a new consideration of heat conduction having a non-local fractional order due to the presence of periodically varying heat sources. Three-phase-lag thermoelastic model, Green Naghdi models II and III (i.e., the models which predicts the...

In this work, a new mathematical model of thermoelasticity theory has been considered in the context of a new consideration of heat conduction with fractional order theory. A functionally graded isotropic unbounded medium is considered subjected to a periodically varying heat source in the context of space-time non-local generalization of three-phase-lag thermoelastic model and Green-Naghdi mod...

This study outlines the local fractional integro-differential equations carried out by the local fractional calculus. The analytical solutions within local fractional Volterra and Abel’s integral equations via the Yang-Laplace transform are discussed. Some illustrative examples will be discussed. The obtained results show the simplicity and efficiency of the present technique with application t...

We study in distributional sense by means of the kernel method an integral transform introduced by Krätzel. It is well known that the cited transform generalizes to the Laplace and Meijer transformation. Properties of analyticity, boundedness, and inversion theorems are established for the generalized transformation. 2000 Mathematics Subject Classification. Primary 44A15, 46F12.

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In this paper we present a time fractional Fokker–Planck equation (fFPE) for radial twophase flow of liquid and gas in porous media. The fFPE of order a is solved for both twoand three-dimensional flow patterns using the Laplace transform method. The general solutions of the fFPE for both twoand threedimensional flows are given as a convolution integral of the input and a kernel in the Laplace ...