ON A BOUNDARY VALUE PROBLEM FOR A TIME-FRACTIONAL WAVE EQUATION WITH THE WEIGHTED RIEMANN-LIOUVILLE AND ATANGANA-BALEANU DERIVATIVES

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Published: iyl 11, 2023
Keywords:
the fractional differential operator, the weighted Atangana-Baleanu fractional derivative, differential equation, Cauchy problem.

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Nargiza Murolimova
Fergana State University

Abstract

In the article a boundary value problem has been formulated and studied for a wave equation involving Riemann-Liuville and Atangana-Baleanu fractional operators with weight functions. The problem was investigated using the Fourier method. In this case, a solution of the problem with respect to the time variable was found using the Laplace transform. The solution to the problem has been represented by series.

Article Details

How to Cite
Murolimova, N. (2023). ON A BOUNDARY VALUE PROBLEM FOR A TIME-FRACTIONAL WAVE EQUATION WITH THE WEIGHTED RIEMANN-LIOUVILLE AND ATANGANA-BALEANU DERIVATIVES. Scientific Journal of the Fergana State University, 28(3), 41. Retrieved from https://journal.fdu.uz/index.php/sjfsu/article/view/1880
Issue
No. 3 (2022): Scientific journal of the Fergana State University
Section
Mathematics
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This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Author Biography

Nargiza Murolimova, Fergana State University

Farg‘ona davlat universiteti o‘qituvchisi

References

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I. K.Allen, D.Duggal, S.Nasir, E. T.Karimov On a boundary value problem for a time-fractional wave equation with the Riemann-Liouville and Atangana-Baleanu derivatives. Bulletin of the Institute of Mathematics, 2020, No1, pp.1-9(Riman-Liuvil va Atangana-Baleanu kasr tartibli differensial operator bilan to‘lqin tenglamasi uchun chegaraviy masala bo‘yicha).

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