q-SUMUDU AND q-LAPLACE TRANSFORMS OF THE BASIC ANALOGUE OF ALEPH-FUNCTION

2019 ◽  
Vol 118 (2) ◽  
pp. 189-211
Author(s):  
Altaf Ahmad Bhat ◽  
Garima Singh ◽  
Renu Jain ◽  
D. K. Jain
Keyword(s):  
Laplace Transforms ◽  
Basic Analogue

scholarly journals On (p,q)-Sumudu and (p,q)-Laplace Transforms of the Basic Analogue of Aleph-Function

Symmetry ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 390
Author(s):  
Asifa Tassaddiq ◽  
Altaf Ahmad Bhat ◽  
D. K. Jain ◽  
Farhad Ali
Keyword(s):  
Integral Transforms ◽  
Laplace Transforms ◽  
General Nature ◽  
Quantum Calculus ◽  
Several Variables ◽  
Basic Analogue

In this paper, we introduce the definitions of Sumudu and Laplace transforms of first and second kind in quantum calculus by using functions of several variables. On account of the general nature of the ( p , q ) -analogue of Aleph-function, a large number of new and known results for these transforms were obtained. Also, we obtain some interesting relationships and identities for these transforms. We also derive some correlations among Aleph function and the above-mentioned integral transforms in quantum calculus.

scholarly journals The Bateman Functions Revisited after 90 Years—A Survey of Old and New Results

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1273
Author(s):  
Alexander Apelblat ◽  
Armando Consiglio ◽  
Francesco Mainardi
Keyword(s):  
Hypergeometric Function ◽  
Laplace Transforms ◽  
Confluent Hypergeometric Function ◽  
Integral Function ◽  
Basic Properties ◽  
Differential Relations

The Bateman functions and the allied Havelock functions were introduced as solutions of some problems in hydrodynamics about ninety years ago, but after a period of one or two decades they were practically neglected. In handbooks, the Bateman function is only mentioned as a particular case of the confluent hypergeometric function. In order to revive our knowledge on these functions, their basic properties (recurrence functional and differential relations, series, integrals and the Laplace transforms) are presented. Some new results are also included. Special attention is directed to the Bateman and Havelock functions with integer orders, to generalizations of these functions and to the Bateman-integral function known in the literature.

A method for evaluating laplace transforms and other integrals

1997 ◽  
Vol 5 (3-4) ◽  
pp. 161-184
Author(s):  
M.L. Glasser ◽  
V. Kowalenko
Keyword(s):  
Laplace Transforms

Closed-form representations of the laplace transforms of bessel funtions

2000 ◽  
Vol 9 (3) ◽  
pp. 217-228 ◽  
Author(s):  
Klaus Rottbrand ◽  
Christian Weddigen
Keyword(s):  
Closed Form ◽  
Laplace Transforms

Tauberian theorems in a Banach lattice, with applications to the LP spaces

1954 ◽  
Vol 50 (2) ◽  
pp. 242-249
Author(s):  
D. C. J. Burgess
Keyword(s):  
Banach Space ◽  
Banach Lattice ◽  
Laplace Transforms ◽  
Tauberian Theorems ◽  
General Argument ◽  
Arbitrary Banach Space ◽  
Lp Spaces ◽  
Special Case

In a previous paper (2) of the author, there was given a treatment of Tauberian theorems for Laplace transforms with values in an arbitrary Banach space. Now, in § 2 of the present paper, this kind of technique is applied to the more special case of Laplace transforms with values in a Banach lattice, and investigations are made on what additional results can be obtained by taking into account the existence of an ordering relation in the space. The general argument is again based on Widder (5) to which frequent references are made.

A General Theorem in Laplace Transforms

1946 ◽  
Vol 30 (289) ◽  
pp. 85 ◽  
Author(s):  
N. W. McLachlan
Keyword(s):  
General Theorem ◽  
Laplace Transforms
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