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

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Scientific Reports of Fergana State University

Scientific Reports of Fergana State University

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ARTICLE ANNOTATION

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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.

AUTHORS

N.Murolimova

Fergana State University

Tags

# дифференциальное уравнение# differensial tenglama# kasr tartibli differensial opera# vazn funksiyasiga ega bo‘lgan At# дифференциальный оператор дробно# дифференциальный оператор Атанга# the fractional differential oper# the weighted Atangana-Baleanu fr# differential equation

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Article Identifiers

ROI:

https://eroi.uz/11.0106/A1022-0028

DOI:

Not Available

References

1. M. Al-Refai On weighted Atangana–Baleanu fractional operators // Advances in Difference Equations. 2020. 3, 11 pp(Vazn funksiyasiga ega bo‘lgan Atangana-Baleanu operatorlar).

2. A.Kilbas,, H. Srivastava, J.Trujillo, Theory and Applications of Fractional Differential Equations. North-Holland Mathematics Studies, vol. 204. Elsevier, Amsterdam, 2006(Kasr tartibli differensial tenglamalar nazariyasi va qo‘llanishi).

3. 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).

4. H. Alzer “Sharp inequalities for the beta function.” 2001. pp.15-21(Beta funksiyasi uchun tengsizliklar).