International Research Journal of Engineering and Technology (IRJET) Volume: 12 Issue:10 | Oct 2025
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e-ISSN: 2395-0056 p-ISSN: 2395-0072
A Study on Integral Transform of the Generalized Lommel Wright KFunction Sapna Chanderiya1, Dr. Indu bala bapna2 1Department of Mathematics, Maharshi Dayanand Saraswati University, Ajmer, Rajasthan, India 2 Department of Mathematics, Maharshi Dayanand Saraswati University, Ajmer, Rajasthan, India
Corresponding Author: sapnachanderiya5@gmail.com ---------------------------------------------------------------------***---------------------------------------------------------------------
Abstract – In the present work we introduces an integral transform of the lommel wright k- function. These transform are expressed in terms of the wright hypergeometric k-function. various interesting transform as the consequence of this method are obtained. which plays an important role to solve the differential equation and also some relations and results related to this generalized lommel wright k-function.
Key Words: Generalized Lommel Wright K-function, Euler Beta Transform, Laplace Transform, K-Transform, Hankel Transform. MSC2020 classification:33E20,33B15,44A10,44A05,44A20.
1.INTRODUCTION In recent years the fractional calculus has become one of the most rapidly growing research subject of mathematical analysis due to its numerous applications in various parts of science as well as mathematics. The transform defined by the following Integral equation
is called the Euler Beta transform with p as a complex parameter. The Laplace transform of a function f(x) is defined by
Where p is a complex parameter. The transform
is called the K-transform with p as a complex parameter and Macdonald function,see(Mathai et al,2010,p.53).
is called the modified Bessel function of the third kind or the
The Hankel transform of a function f(x) denoted by g(p,v) defined as
where
is called the Bessel-Maitland function or the maitland Bessel function (Mathai et al, 2010, p.22 and p.56).
Next for the result of this paper. we take The Wright Hypergeometric function in series form [9], denoted by as:
where the cofficient
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and
are positive real numbers such that.
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is define