Ahmed Fitouhi, Iness Jebabli, Elina L. Shishkina, Sergei M. Sitnik
Abstract:
In this article we study applications of integral transforms composition
method (ITCM) for obtaining transmutations via integral transforms.
It is possible to derive wide range of transmutation operators by this
method. Classical integral transforms are involved in the integral
transforms composition method (ITCM) as basic blocks, among them are Fourier,
sine and cosine-Fourier, Hankel, Mellin, Laplace and some generalized transforms.
The ITCM and transmutations obtaining by it are applied to deriving
connection formulas for solutions of singular differential equations and
more simple non-singular ones. We consider well-known classes of singular
differential equations with Bessel operators, such as classical and
generalized Euler-Poisson-Darboux equation and the generalized
radiation problem of A.Weinstein. Methods of this paper are applied to
more general linear partial differential equations with Bessel operators,
such as multivariate Bessel-type equations, GASPT (Generalized Axially
Symmetric Potential Theory) equations of Weinstein, Bessel-type
generalized wave equations with variable coefficients,ultra B-hyperbolic
equations and others. So with many results and examples the main
conclusion of this paper is illustrated:
the integral transforms composition method (ITCM) of constructing transmutations
is very important and effective tool also for obtaining connection formulas
and explicit representations of solutions to a wide class of singular
differential equations, including ones with Bessel operators.
Submitted May 22, 2018. Published June 25, 2018.
Math Subject Classifications: 26A33, 44A15.
Key Words: Transmutations; integral transforms composition method;
Bessel operator; wave-type equation; singular differential equation;
Hankel transform.
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Ahmed Fitouhi University of Tunis El Manar Tunis, Tunisia email: Ahmed.Fitouhi@fst.rnu.tn |
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Inèss Jebabli University of Tunis El Manar Tunis, Tunisia email: jebabli.iness@hotmail.fr |
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Elina L. Shishkina Voronezh State University Voronezh, Russia email: ilina_dico@mail.ru |
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Sergei M. Sitnik Belgorod State National Research University (BSU) Belgorod, Russia email: sitnik@bsu.edu.ru |
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