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Ushbu maqolada vazn funksiyasiga ega bo‘lgan Riman-Liuvil va Atangana-Baleanu kasr tartibli operatorlar
qatnashgan to‘lqin tenglamasi uchun bir chegaraviy masala bayon qilingan va o‘rganilgan. Masala Furye usuli yordamida
tadqiq qilingan. Bunda vaqt o‘zgaruvchisi bo‘yicha hosi lqilingan masala yechimi Laplas almashtirishi yordamida topilgan.
Qo‘yilgan masalaning yechimi qator ko‘rinishida topilgan.

  • Web Address
  • DOIhttps://doi.org/10.56292/SJFSU/vol28_iss3/a41
  • Date of creation in the UzSCI system 03-10-2022
  • Read count 250
  • Date of publication 23-09-2022
  • Main LanguageO'zbek
  • Pages214-222
Ўзбек

Ushbu maqolada vazn funksiyasiga ega bo‘lgan Riman-Liuvil va Atangana-Baleanu kasr tartibli operatorlar
qatnashgan to‘lqin tenglamasi uchun bir chegaraviy masala bayon qilingan va o‘rganilgan. Masala Furye usuli yordamida
tadqiq qilingan. Bunda vaqt o‘zgaruvchisi bo‘yicha hosi lqilingan masala yechimi Laplas almashtirishi yordamida topilgan.
Qo‘yilgan masalaning yechimi qator ko‘rinishida topilgan.

Русский

В данной статье была исследована и изучена одна граничная задача для уравнения колебания, с
участием дробного оператора Римана-Лиувилля и Атангана-Балеану, имеющий функцию с весом. Задача
была решена методом Фурье. При нахождении решения задачи, использована преобразование Лапласа
относительно временной переменной. Решение поставленной задачи было найдено в виде ряда.

English

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.

№ Author name position Name of organisation
1 Murolimova N.A. 1 Fergana State University
№ Name of reference
1 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 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 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 4. H. Alzer “Sharp inequalities for the beta function.” 2001. pp.15-21(Beta funksiyasi uchun tengsizliklar).
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