5 citations · 13 across the 13 of their papers we have counts for
13 papers
On the -analogue of Duhamel's principle
Mohammed Elamine Sebih, Serikbol Shaimardan, Irfan Ali
In this paper, we revisit the classical Duhamel's principle and provide a self-contained proof of this fundamental tool for linear evolution equations and systems of coupled equati…
Fujita exponents on quantum Euclidean spaces
Edward McDonald, Michael Ruzhansky, Serikbol Shaimardan +1
We study the well-posedness of a non-linear heat equation with power nonlinearity with positive initial data on quantum Euclidean spaces. We prove a noncommutative analogue of the…
Fourier multipliers and their applications to PDE on the quantum Euclidean space
M. Ruzhansky, S. Shaimardan, K. Tulenov
In this work, we present some applications of the - boundedness of Fourier multipliers to PDEs on the noncommutative (or quantum) Euclidean space. More precisely, we esta…
Sobolev inequality and its applications to nonlinear PDE on noncommutative Euclidean spaces
Michael Ruzhansky, Serikbol Shaimardan, Kanat Tulenov
In this work, we study the Sobolev inequality on noncommutative Euclidean spaces. As a simple consequence, we obtain the Gagliardo-Nirenberg type inequality and as its application…
Hörmander type Fourier multiplier theorem and Nikolskii inequality on quantum tori, and applications
Michael Ruzhansky, Serikbol Shaimardan, Kanat Tulenov
In this paper, we study Hörmander type Fourier multiplier theorem and the Nikolskii inequality on quantum tori. On the way to obtain these results, we also prove some classical ine…
Some estimates for Mittag-Leffler function in quantum calculus and applications
Michael Ruzhansky, Serikbol Shaimardan, Niyaz Tokmagambetov
The study of the Mittag-Leffler function and its various generalizations has become a very popular topic in mathematics and its applications. In the present paper we prove the foll…
Well-posedness of heat and wave equations generated by Rubin's q-difference operator in Sobolev spaces
Serikbol Shaimardan, Lars-Erik Persson, Niyaz Tokmagambetov
In this paper, we investigate difference-differential operators of parabolic and hyperbolic types. Namely, we consider non-homogenous heat and wave equations for Rubin's difference…
The Prabhakar fractional -integral and -differential operators, and their properties
Serikbol Shaimardan, Erkinjon Karimov, Michael Ruzhansky +1
In this paper, we have introduced the Prabhakar fractional -integral and -differential operators. We first study the semi-group property of the Prabhakar fractional -integ…
Direct and inverse source problems for heat equation in quantum calculus
Michael Ruzhansky, Serikbol Shaimardan
In this paper we explore the weak solutions of the Cauchy problem and an inverse source problem for the heat equation in the quantum calculus, formulated in abstract Hilbert spaces…
Fractional Cauchy problems associated with the bi-ordinal Hilfer fractional -derivative
Erkinjon Karimov, Michael Ruzhansky, Serikbol Shaimardan
To study the existence and uniqueness of solutions to Cauchy-type problems for fractional q-difference equations with the bi-ordinal Hilfer fractional q-derivative which is an exte…
Inverse problems for q-analogue of the heat equation
Erkinjon Karimov, Serikbol Shaimardan
In this paper we explore the weak solution of a time-dependent inverse source problem and inverse initial problem for -analogue of the heat equation. As an over-determination co…
Wave equation for Sturm-Liouville operator with singular potentials
Michael Ruzhansky, Serikbol Shaimardan, Alibek Yeskermessuly
The paper is denoted to the initial-boundary value problem for the wave equation with the Sturm-Liouville operator with irregular (distributive) potentials. To obtain a solution to…
Existence and uniqueness of some Cauchy Type Problems in fractional q-difference calculus
Lars-Erik Persson, Serikbol Shaimardan, Nariman Sarsenovich Tokmagambetov
In this paper we derive a sufficient condition for the existence of a unique solution of a Cauchy type q-fractional problem (involving the fractional q-derivative of Riemann-Liouvi…