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Solvability of a Non-local Problem with Integral Transmitting Condition for Mixed Type Equation with Caputo Fractional Derivative

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Abstract

In the present paper, we discuss solvability questions of a non-local problem with integral form transmitting conditions for a mixed parabolic–hyperbolic type equation with the Caputo fractional derivative in a domain bounded by smooth curves. A uniqueness of the solution for a formulated problem we prove using energy integral method with some modifications. The existence of solution will be proved by equivalent reduction of the studied problem into a system of second kind Fredholm integral equations.

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Authors and Affiliations

  1. Department of Mathematics, Anand International College of Engineering, Jaipur, India

    Praveen Agarwal

  2. Kazakh National Pedagogical, University Named After Abai, Almaty, Kazakhstan

    Abdumauvlen Berdyshev

  3. Institute of Mathematics, National University of Uzbekistan, Tashkent, Uzbekistan

    Erkinjon Karimov

Authors
  1. Praveen Agarwal
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  2. Abdumauvlen Berdyshev
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  3. Erkinjon Karimov
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Corresponding author

Correspondence to Erkinjon Karimov.

Additional information

This work was completed with the support of the Ministry of education and science of the Republic of Kazakhstan, Grant No. 3293/GF4.

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Agarwal, P., Berdyshev, A. & Karimov, E. Solvability of a Non-local Problem with Integral Transmitting Condition for Mixed Type Equation with Caputo Fractional Derivative. Results Math 71, 1235–1257 (2017). https://doi.org/10.1007/s00025-016-0620-1

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  • DOI: https://doi.org/10.1007/s00025-016-0620-1

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