Adyghe Int. Sci. J. Vol. 23, No 4. P. 62-68. 

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DOI: https://doi.org/10.47928/1726-9946-2023-23-4-62-68
EDN: QAYMBW

MATHEMATICS

MSC 26A33, 34B05

Original Article

On the question of solving a mixed boundary value problemfor an equation with fractional derivatives

with different origins

Liana Magometovna Eneeva
Ph.D. in physics and mathematics, senior Researcher of Department of mathematical modeling of geophysical processes, Institute of Applied Mathematics and Automation of KBSC RAS, (360017, 89 А Shortanova St., Nalchik, Russia), https://orcid.org/0000-0003-2530-5022, eneeva72@list.ru

Abstract. An approach to solving boundary value problems for an ordinary differential equation of fractional order containing a composition of left- and right-handed Riemann-Liouville and Caputo fractional differentiation operators is proposed. The approach is based on the reduction of the equation under consideration to the study of integral equations of fractional order with involution. As an example, a mixed problem has been solved. In particular, the proposed approach allows us to improve the previously obtained conditions for the solvability of this problem.

Keywords: fractional differential equation with different origins, equation with involution, mixed boundary value problem, Riemann-Liouville derivative, Caputo derivative.

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

For citation. Eneeva L. M. On the question of solving a mixed boundary value problem for an equation with fractional derivatives with different origins. Adyghe Int. Sci. J. 2023. Vol. 23, No. 4. P. 62–68.
DOI: https://doi.org/10.47928/1726-9946-2023-23-4-62-68; EDN: QAYMBW

The author has read and approved the final version of the manuscript.
Submitted 18.11.2023; approved after reviewing 15.12.2023; aeeepted for publication 18.12.2023.

© Eneeva L. M., 2023

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