VAZN FUNKSIYASIGA EGA BO‘LGAN RIMAN-LIUVIL VA ATANGANA-BALEANU KASR TARTIBLI OPERATORLAR QATNASHGAN TO‘LQIN TENGLAMASI UCHUN CHEGARAVIY MASALA
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Annotatsiya
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.
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Foydalaniladigan adabiyotlar
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).
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).
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).
H. Alzer “Sharp inequalities for the beta function.” 2001. pp.15-21(Beta funksiyasi uchun tengsizliklar).