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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.

  • Internet ҳавола
  • DOI
  • UzSCI тизимида яратилган сана 15-08-2022
  • Ўқишлар сони 0
  • Нашр санаси 28-08-2019
  • Мақола тилиRus
  • Саҳифалар сони10-14
Ўзбек

Мақолада икки тартибли Хилфер ҳосилали суб-диффузия ва классик тўлқин тенгламасида иборат аралаш типдаги тенглама учун Трикоми типидаги масала аралаш соҳада ўрганилган. Асосий қўлланилган усуллар интеграл тенгламалар ва энергия интеграллари усулларидир.

Русский

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.

English

В статье рассмотрена задача типа Трикоми для уравнения смешанного типа с уравнением суб- диффузии и волновым уравнением. Основными методами являются метод интегральных уравнений и метод интегралов энергии.
 

№ Ҳавола номи
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10 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 11. Hilfer R. Applications of Fractional Calculus in Physics. Singapore: World Scientific, 2000.
12 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 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 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.
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