INTEGRAL REPRESENTATIONS OF MITTAG-LEFFLER TYPE FUNCTIONS

1. Uchaikin V.V. Fractional derivatives for physicists and engineers. Vol. I,II. Springer, Heidelberg, 2013.

2. Kilbas A.A, Srivastava H.M, Trujillo J.J. Theory and applications of fractional differential equations. Elsevier, Amsterdam, 2006.

3. Podlubny I. Fractional differential equations. An introduction to fractional derivateves, fractional differential equations, to methods of their solution and some applications. Academic Press, San Diego, 1999.

4. Gorenflo R., Kilbas A. A., Mainardi F. Mittag-Leffler functions related topics and applications. Springer, Berlin, 2014.

5. Mainardi F., Pagnini G. The role of the Fox-Wright functions in fractional sub-diffusion of distributed order. Journal of Computational and Applied Mathematics, 2007,2, pp. 245-257.

6. Praphakar T.R. A singular integral equation with a generalized Mittag-Leffler function in the kernel. Yokohama math. J. 1971, 19, pp. 7-15.

7. Pskhu A.V. Partial Differential Equations of Fractional Order. Nauka, Moscow, 2005.

8. Karimov E, Al-Salti N, Kerbal S. An inverse source non-local problem for a mixed type equation with a Caputo fractional differential operator. East Asian journal of Applied Mathematics, 2017, 2, pp. 417-438.

9. Salakhitdinov M.S, Karimov E.T. Direct and inverse source problems for two-term time fractional diffusion equation with Hilfer derivative. Uzbek Mathematical Journal, 2017, 4. pp. 140-149.

10. Karimov E.T, Kerbal S. Tricomi type problem for mixed type equation with sub-diffusion and wave equation. FDU. Ilmiy Khabarlar, 2019, 3, pp. 10-14.

11. Allen I.K, Doggal D, Nasir S, Karimov E. On a boundary value problem for a time- fractional wave equation with the Riemann-Liouville and Atangana-Baleanu derivatives. Bulletin of the Institute of Mathematics, 2020, 1, pp. 1-9.