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Finite Fractional Sturm-Liouville Transforms For Generalized Fractional Derivatives | ||
| Iranian Journal of Science | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 25 بهمن 1394 | ||
| نوع مقاله: Regular Paper | ||
| شناسه دیجیتال (DOI): 10.22099/ijsts.2016.3577 | ||
| نویسندگان | ||
| Shiva Eshaghi1؛ Alireza Ansari* 2 | ||
| 1Department of Applied Mathematics, Faculty of Mathematical Sciences, Shahrekord University, P.O. Box 115, Shahrekord, Iran | ||
| 2Department of Applied Mathematics, Faculty of Mathematical Sciences, Shahrekord University, P.O.Box 115, Shahrekord, Iran | ||
| چکیده | ||
| In this article, we introduce the regular and singular fractional Sturm-Liouville problems with the Hilfer and Hilfer-Prabhakar derivatives. We show that these problems with corresponding boundary conditions have real eigenvalues and their eigenfunctions are orthogonal. Also, the finite fractional Sturm-Liouville transforms and their inversion formulas are established, and as an application, the formal solution of the fractional Laplace equation in prolate spheroidal coordinates is obtained using the finite Legendre transform. | ||
| کلیدواژهها | ||
| Sturm-Liouville problem؛ Finite transform؛ Legendre transform؛ Hilfer-Prabhakar derivative | ||
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