A transition integral transform obtained from generalization of the Fourier transform

Wolf, 1979 Bracewell, 2000 Christensen, 2010 Duffy, 2000 Duffy, 2004 Poularikas, 2000 Debnath, 2007 De Bie H, Oste R, Van der Jeugt J. Generalized Fourier transforms arising from the enveloping algebras of SL(2) and OSP(1/2). Int Math Res Not; 2016. p. 4649–705. Howe R. The oscillator semigroup. The mathematical heritage of Hermann Weyl. In: Proc sympos pure math; 1988. p. 61–132. Ozaktas, 2001 Weerakoon, 1994, Application of Sumudu transform to partial differential equations, Int J Math Educ Sci Technol, 25, 277, 10.1080/0020739940250214 Weerakoon, 1998, Complex inversion formula for Sumudu transform, Int J Math Educ Sci Technol, 4, 618 Jit Singh, 2009, Beyond fractional derivatives: local approximation of other convolution integrals, Proc R Soc A, 466, 563, 10.1098/rspa.2009.0378 Andrzej HY, 2002, Multidimensional solutions of space fractional diffusion equations, Proc R Soc A, 458, 1248 Spence, 2010, A new transform method I: domain-dependent fundamental solutions and integral representations, Proc R Soc A, 466, 2259, 10.1098/rspa.2009.0512 Spence, 2010, A new transform method II: the global relation and boundary-value problems in polar coordinates, Proc R Soc A, 466, 2283, 10.1098/rspa.2009.0513 Fokas, 1993, Integral transforms, spectral representation and the d-bar problem, Proc R Soc A, 443, 2187 Zianea, 2017, Local fractional Sumudu decomposition method for linear partial differential equations with local fractional derivative, J King Saud Univ Al-Omari, 2016, On q-analogues of the Mangontarum transform for certain q-Bessel functions and some application, J King Saud Univ – Sci, 28, 10.1016/j.jksus.2015.04.008 Shijun, 2003 Yang, 2017, A new integral transform operator for solving the heat-diusion problem, Appl Math Lett, 64, 193, 10.1016/j.aml.2016.09.011 Yang, 2017, New integral transforms for solving a steady heat transfer problem, Therm Sci, 21, 79, 10.2298/TSCI17S1079Y