Scientific journal of the Fergana State University


In this paper, we have considered a Tricomi type problem for mixed type equation with Hilfer’s double order derivative sub-diffusion equation and classical wave equation in a composite domain. Main methods of the investigation are a method of integral equations and energy integrals’ method.

First Page


Last Page





Uchaikin V. V. Fractional Derivatives for Physicists and Engineers. Vol. I: Background and Theory. Vol. II: Applications. Nonlinear Physical Science. Heidelberg: Springer and Higher Education Press, 2012. 2. Kilbas A. A., Srivastava H. M., Trujillo J. J. Theory and Applications of Fractional Differential Equations, volume 204. North-Holland Mathematics Studies. -Amsterdam: Elsevier, 2006. 3. Luchko Y., Gorenflo R. An operational method for solving fractional differential equations with the Caputo derivatives. Acta Mathematica Vietnamica, 24, 1999, pp.207- 233. 4. Sandev T., Metzler R., Tomovski Z. Fractional diffusion equation with a generalized Riemann-Liouville time fractional derivative. J. Phys. A: Math. Theor. 44, 2011, 255203 (21pp) 5. Pskhu A. V. Partial Differential Equations of Fractional Order (In Russian). Moscow: Nauka, 2005. 6. Gekkieva S. Kh. A boundary value problem for the generalized transfer equation with a fractional derivative in a semi-infinite domain (In Russian). Izv. Kabardino-Balkarsk. Nauchnogo Tsentra RAN 1(8), 2002, pp.6-8. 7. Kilbas A. A., Repin O. A. An analog of the Tricomi problem for a mixed type equation with a partial fractional derivative. Fract. Calc. Appl. Anal. 13(1), 2010, p.69-84 8. Berdyshev A. S., Cabada A., Karimov E. T. On a non-local boundary problem for a parabolic-hyperbolic equation involving Riemann-Liouville fractional differential operator. Nonlinear Analysis, 75, 2012, pp.3268-3273. 9. Agarwal P., Berdyshev A. S., Karimov E. T. Solvability of a non-local problem with integral transmitting condition for mixed type equation with Caputo fractional derivative. Results in Mathematics. 71(3), 2017, pp. 1235-1257 10. Karimov E. T., Berdyshev A. S., Rakhmatullaeva N. A. Unique solvability of a non-local problem for mixed-type equation with fractional derivative. Mathematical Methods in the Applied Sciences. 40(8), 2017, pp.2994-2999 11. Hilfer R. Applications of Fractional Calculus in Physics. Singapore: World Scientific, 2000. 12. Hilfer R., Luchko Y., Tomovski ˇZ. Operational method for the solution of fractional differential equations with generalized Riemann-Liouville fractional derivatives. Fract. Calc. Appl. Anal. 12(3), 2009, pp.299-318 13. Bulavitsky V.M. Closed form of the solutions of some boundary-value problems for anomalous diffusion equation with Hilfer’s generalized derivative. Cybernetics and Systems Analysis, Vol.30, No 4, 2014, 570-577. 14. Karimov E.T. Tricomi type boundary value problem with integral conjugation condition for a mixed type equation with Hilfer fractional operator. Bulletin of the Institute of Mathematics, No 1, 2019, 19-26.

Included in

Mathematics Commons



To view the content in your browser, please download Adobe Reader or, alternately,
you may Download the file to your hard drive.

NOTE: The latest versions of Adobe Reader do not support viewing PDF files within Firefox on Mac OS and if you are using a modern (Intel) Mac, there is no official plugin for viewing PDF files within the browser window.