ON A BOUNDARY VALUE PROBLEM FOR A TIME-FRACTIONAL WAVE EQUATION WITH THE WEIGHTED RIEMANN-LIOUVILLE AND ATANGANA-BALEANU DERIVATIVES
Keywords:
the fractional differential operator, the weighted Atangana-Baleanu fractional derivative, differential equation, Cauchy problem.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.
References
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).
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