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The fundamental solutions to the corresponding Cauchy and source problems in the case of one spatial variable are studied using the Laplace transform with respect to time and the Fourier transform with respect to the spatial coordinate. The numerical results are illustrated graphically.<\/jats:p>","DOI":"10.3390\/e19070297","type":"journal-article","created":{"date-parts":[[2017,6,23]],"date-time":"2017-06-23T08:16:18Z","timestamp":1498205778000},"page":"297","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":22,"title":["Two Approaches to Obtaining the Space-Time Fractional Advection-Diffusion Equation"],"prefix":"10.3390","volume":"19","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7492-5394","authenticated-orcid":false,"given":"Yuriy","family":"Povstenko","sequence":"first","affiliation":[{"name":"Institute of Mathematics and Computer Sciences, Faculty of Mathematical and Natural Sciences, Jan D\u0142ugosz University in Cz\u0229stochowa, al. Armii Krajowej 13\/15, 42-200 Cz\u0229stochowa, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tamara","family":"Kyrylych","sequence":"additional","affiliation":[{"name":"Institute of Law, Administration and Management, Faculty of Philology and History, Jan D\u0142ugosz University in Cz\u0229stochowa, Zbierskiego 2\/4, 42-200 Cz\u0229stochowa, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2017,6,23]]},"reference":[{"key":"ref_1","unstructured":"Risken, H. (1989). The Fokker-Planck Equation. Methods of Solution and Applications, Springer. [2nd ed.]."},{"key":"ref_2","unstructured":"Frank, T.D. (2005). Nonlinear Fokker-Planck Equations. Fundamentals and Applications, Springer."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Van Kampen, N.G. (2007). Stochastic Processes in Physics and Chemistry, Elsevier. 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