Korean J. Math. Vol. 27 No. 2 (2019) pp.487-503
DOI: https://doi.org/10.11568/kjm.2019.27.2.487

Certain results involving fractional operators and special functions

Article Sidebar

PDF
Published: Jun 30, 2019
Keywords:
Laplace transforms, Fourier transforms, Kr\"atzel function, Hankel transforms, Riemann - Liouville fractional derivative.
Mathematics Subject Classification:
26A33, 44A10, 44A15, 44A35

Main Article Content

Arman Aghili
Department of Applied Mathematics Faculty of Mathematical Science University of Guilan, Rasht - Iran, P.O.BOX 1841

Abstract

In this study, the author provided a discussion on one dimensional Laplace and Fourier transforms with their applications. It is shown that the combined use of exponential operators and integral transforms provides a powerful tool to solve space fractional partial differential equation with non - constant coefficients. The object of the present article is to extend the application of the joint Fourier - Laplace transform to derive an analytical solution for a variety of time fractional non - homogeneous KdV. Numerous exercises and examples presented throughout the paper.



Article Details

Supporting Agencies

University of Guilan

References

[1] A.Aghili, Special functions, integral transforms with applications, Tbilisi Mathematical Journal 12 (1) (2019), 33–44. Google Scholar

[2] A.Aghili, Fractional Black–Scholes equation, International Journal of Financial Engineering 4 (1) (2017), World Scientific Publishing Company, DOI:10.1142/S2424786317500049 Google Scholar

[3] A.Apelblat, Laplace transforms and their applications, Nova science publishers, Inc, New York, 2012. Google Scholar

[4] G.Dattoli, methods, fractional operators and special polynomials, Applied Math- ematics and computations 141 (2003), 151–159. Google Scholar

[5] G.Dattoli, H.M.Srivastava and K.V.Zhukovsky, Operational methods and differ- ential equations to initial value problems, Applied Mathematics and computa- tions 184 (2007), 979–1001. Google Scholar

[6] G.Dattoli, P.E.Ricci, C.Cesarano, and L.Vasquez, Mathematical and computer modelling 37 (2003), 729–733. Google Scholar

[7] H.J. Glaeske, A.P. Prudnikov and K.A.Skornik, Operational calculus and related topics, Chapman and Hall/CRC, USA, (2006). Google Scholar

[8] A.A.Kilbas, H.M.Srivastava and J.J.Trujillo, Theory and applications of fractional differential equations, Elsevier.B.V, Amsterdam, (2006). Google Scholar

[9] I. Podlubny, Fractional differential equations, Academic Press, San Diego, CA, 1999. Google Scholar

[10] F. Usta, H. Budak and M.Z. Sarikaya, Yang-Laplace Transform Method Volterra and Abels Integro-Differential Equations of Fractional Order, International Jour- nal of Nonlinear Analysis and Applications 9 (2) (2017), 203–214. DOI: 10.22075/ijnaa.2018.13630.1709 Google Scholar