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Adyghe Int. Sci. J. Vol. 23, No 4. P. 16-22

Adyghe Int. Sci. J. Vol. 23, No 4. P. 16-22. 

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MSC 34A08, 34B05 Original Article

On the correctness of initial problems for the fractional
diffusion equation

Fatima Takhirovna Bogatyreva
Junior researcher, Institute of Applied Mathematics and Automation, KBSC RAS (360000, Russia, Nalchik, Shortanova St. 89 A), ORCID,

Abstract. The paper studies a second-order parabolic partial differential equation with fractional differentiation with respect to a time variable. The fractional differentiation operator is a linear combination of the Riemann-Liouville and Gerasimov-Caputo fractional derivatives. It is shown that the distribution of orders of fractional derivatives, included in the equation affects the correctness of the initial problems for the equation under consideration.

Keywords: fractional diffusion equation, Riemann–Liouville operator, Gerasimov–Caputo operator, fractional derivative, Wright function.

Acknowledgments: the author are thankful to the anonymous reviewer for his valuable remakes.

For citation. Bogatyreva F. T. On the correctness of initial problems for the fractional diffusion equation. Adyghe Int. Sci. J. 2023. Vol. 23, No. 4. P. 16–22. DOI:; EDN: ECLJES

The author has read and approved the final version of the manuscript.
Submitted 18.12.2023; approved after reviewing 21.12.2023; aeeepted for publication 22.12.2023.

© Bogatyreva F. T., 2023


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