Green function of triharmonic heat equation using addition formula of function e^(-x^3)
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In this article, the authors used the Mellin transform of Airy function to derive the Green function of tri-harmonic heat equation in terms of the Airy functions, and used the Hankel functions of first kind to derive this representation.Abstract:
In this paper, using the Mellin transform of Airy function we present an integral addition formula for the function e x 3 . In deriving this representation, we make use of the Hankel functions of first kind and apply this representation to get the Green function of triharmonic heat equation in terms of the Airy functions. 2010 Mathematics Subject Classification: 33C10; 34B27; 35K30read more
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Table Of Integrals Series And Products
TL;DR: The table of integrals series and products is universally compatible with any devices to read and is available in the book collection an online access to it is set as public so you can get it instantly.
Dissertation
Integral transforms and their applications
Abd elgadir,Ahmed Ali Mohammed +1 more
TL;DR: In this paper, the relationship between these transforms and their properties was discussed and some important applications in physics and engineering were given, as well as their properties and applications in various domains.
Journal ArticleDOI
Distributed order fractional diffusion equation with fractional Laplacian in axisymmetric cylindrical configuration
TL;DR: In this paper , the authors considered the fractional and natural powers of the Laplacian operator in axisymmetric cylindrical geometry and derived the fundamental solution of the distributed order time-fractional diffusion equation with this type of fractional LaplACian and the fraction fractional moment of solution.
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Squared radial Ornstein-Uhlenbeck processes and inverse Laplace transforms of products of confluent hypergeometric functions
Leila Moslehi,Alireza Ansari +1 more
TL;DR: In this paper, the squared radial Ornstein-Uhlenbeck process and associated Kolmogorov backward equation (the Laguerre heat equation) were considered and the Green function of the Laplace transform of the transition density function in terms of the con-fluent hypergeometric functions was obtained.
References
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A table of integrals
TL;DR: Basic Forms x n dx = 1 n + 1 x n+1 (1) 1 x dx = ln |x| (2) udv = uv − vdu (3) 1 ax + bdx = 1 a ln|ax + b| (4) Integrals of Rational Functions
Journal ArticleDOI
Handbook of Mathematical Functions with Formulas
TL;DR: The Handbook of Mathematical Functions with Formulas (HOFF-formulas) as mentioned in this paper is the most widely used handbook for mathematical functions with formulas, which includes the following:
Table Of Integrals Series And Products
TL;DR: The table of integrals series and products is universally compatible with any devices to read and is available in the book collection an online access to it is set as public so you can get it instantly.
Book
Airy functions and applications to physics
Oliveier Vallée,Manuel Soares +1 more
TL;DR: In this paper, an exhaustive compilation of the current knowledge on the analytical properties of Airy functions, developing with care the calculus implying the Airy function, is provided, which is divided into two parts: the first is devoted to the mathematical properties of airy functions and the second presents some applications of airys to various fields of physics.
Dissertation
Integral transforms and their applications
Abd elgadir,Ahmed Ali Mohammed +1 more
TL;DR: In this paper, the relationship between these transforms and their properties was discussed and some important applications in physics and engineering were given, as well as their properties and applications in various domains.