Blar i forfatter Artikler, rapporter og annet (datateknologi og beregningsorienterte ingeniørfag) "Shaimardan, Serikbol"

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    • Hardy-type inequalities in fractional h-discrete calculus 

      Persson, Lars Erik; Oinarov, Ryskul; Shaimardan, Serikbol (Journal article; Tidsskriftartikkel; Peer reviewed, 2018-04-04)
      The first power weighted version of Hardy’s inequality can be rewritten as [<i>mathematical formula</i>] where the constant <i>C</i> =[<i>p</i> / <i>p</i> - <i><b>a</b></i> - 1]<sup><i>p</i></sup> is sharp. This inequality holds in the reversed direction when<math xmlns="http://www.w3.org/1998/Math/MathML"> <mn>0</mn> <mo>&#x2264;<!-- ≤ --></mo> <mi><i>p</i></mi> <mo>&lt;</mo> <mn>1</mn> ...

    • On the Heat and Wave Equations with the Sturm-Liouville Operator in Quantum Calculus 

      Shaimardan, Serikbol; Persson, Lars-Erik; Tokmagambetov, Nariman (Journal article; Tidsskriftartikkel; Peer reviewed, 2023-01-19)
      In this paper, we explore a generalised solution of the Cauchy problems for the q-heat and q-wave equations which are generated by Jackson’s and the q-Sturm-Liouville operators with respect to t and x, respectively. For this, we use a new method, where a crucial tool is used to represent functions in the Fourier series expansions in a Hilbert space on quantum calculus. We show that these solutions ...

    • Some new Hardy-type inequalities for Riemann-Liouville fractional q-integral operator 

      Persson, Lars Erik; Shaimardan, Serikbol (Peer reviewed; Journal article; Tidsskriftsartikkel, 2015-09-24)
      We consider the q-analog of the Riemann-Liouville fractional q-integral operator of order n∈Nn∈N. Some new Hardy-type inequalities for this operator are proved and discussed.

    • Well-posedness of heat and wave equations generated by Rubin’s q-difference operator in Sobolev spaces 

      Shaimardan, Serikbol; Persson, Lars-Erik; Tokmagambetov, Niyaz (Journal article; Tidsskriftartikkel; Peer reviewed, 2023)
      In this paper, we investigate difference-differential operators of parabolic and hyperbolic types. Namely, we considern on-homogenous heat and wave equations for Rubin’s difference operator. Wellposedness results are obtained in appropriate Sobolev type spaces. In particular, we prove that the heat and wave equations generated by Rubin’s difference operator have unique solutions. We even show that ...