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Gellerstedt Type Problem for the Loaded Parabolic-Hyperbolic Type Equation with Caputo and Erdelyi–Kober Operators of Fractional Order

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Abstract

The work is devoted to the proof of the uniqueness and existence of solution to local and nonlocal problems with an integral gluing condition for a loaded parabolic-hyperbolic type equation with differential and integral operators of fractional order, in which the trace of the solution appears in the Erdelyi–Kober integral operator. Using the method of energy integrals, the uniqueness of the solution is proved, and the existence of the solution is proved by the method of integral equations.

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Authors and Affiliations

  1. National University of Uzbekistan named after M. Ulugbek, 4 Universitetskaya str., 100174, Tashkent, Republic of Uzbekistan

    O. Kh. Abdullaev & B. I. Islomov

Authors
  1. O. Kh. Abdullaev
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  2. B. I. Islomov
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Correspondence to O. Kh. Abdullaev or B. I. Islomov.

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Russian Text © The Author(s), 2020, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2020, No. 10, pp. 33–46.

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Abdullaev, O.K., Islomov, B.I. Gellerstedt Type Problem for the Loaded Parabolic-Hyperbolic Type Equation with Caputo and Erdelyi–Kober Operators of Fractional Order. Russ Math. 64, 29–42 (2020). https://doi.org/10.3103/S1066369X20100047

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  • DOI: https://doi.org/10.3103/S1066369X20100047

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