65 citations · 296 across the 35 of their papers we have counts for
42 papers
Product Pitt inequalities and signed Boas equivalences for general monotone functions
Niyaz Tokmagambetov
We prove product-weight Pitt inequalities for real or complex functions on whose full mixed Vitali variation satisfies an exterior-tail general monotonicity condition…
Moduli of smoothness and growth of the Laguerre transform: two-sided estimates
Nurbek Kakharman, Niyaz Tokmagambetov
We study weighted coefficient estimates for the Laguerre transform in terms of moduli of smoothness generated by the Laguerre translation. For every integer and $1\le p\le2…
Power-kernel fractional Sturm--Liouville operators: a graph realization and boundary-independent singular-value asymptotics
Niyaz Tokmagambetov
For we construct a closed realization of in whose domain contains the singular mode . The domain, defined via…
Dilation-balanced product Pitt inequalities for mixed-tail potentials
Niyaz Tokmagambetov
Motivated by the one-dimensional and radial theory of general monotone functions, we introduce a natural multiparameter general-monotonicity class for product Fourier inequalities.…
Late-Time Fractional-Order Identification in Caputo Diffusion Equation
Niyaz Tokmagambetov
We study late-time identification of the Caputo order in a linear diffusion equation generated by a strictly positive self-adjoint operator with compact resolvent. For signed scala…
Fractional wave equation with irregular mass and dissipation
Michael Ruzhansky, Mohammed Elamine Sebih, Niyaz Tokmagambetov
In this paper, we pursue our series of papers aiming to show the applicability of the concept of very weak solutions. We consider a wave model with irregular position dependent mas…
One inverse source problem generated by the Dunkl operator
Bayan Bekbolat, Niyaz Tokmagambetov
The aim of this paper is to study time-fractional pseudo-parabolic type equations generated by the Dunkl operator. The forward problem is considered and its well-posedness is estab…
Inverse problem of determining time-dependent leading coefficient in the time-fractional heat equation
Daurenbek Serikbaev, Michael Ruzhansky, Niyaz Tokmagambetov
In this paper, we investigate direct and inverse problems for the time-fractional heat equation with a time-dependent leading coefficient for positive operators. First, we consider…
Heat Source Determining Inverse Problem for non-local in time equation
Daurenbek Serikbaev, Michael Ruzhansky, Niyaz Tokmagambetov
In this paper, we consider the inverse problem of determining the time-dependent source term in the general setting of Hilbert spaces and for general additional data. We prove the…
Schrödinger equation with singular position dependent mass
Michael Ruzhansky, Mohammed Elamine Sebih, Niyaz Tokmagambetov
We consider the Schrödinger equation with singular position dependent effective mass and prove that it is very weakly well posed. A uniqueness result is proved in an appropriate se…
Heat equation with singular thermal conductivity
Michael Ruzhansky, Mohammed Elamine Sebih, Niyaz Tokmagambetov
In this paper, we study the heat equation with an irregular spatially dependent thermal conductivity coefficient. We prove that it has a solution in an appropriate very weak sense.…
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 heat equation with singular potentials. II: Hypoelliptic case
Marianna Chatzakou, Michael Ruzhansky, Niyaz Tokmagambetov
In this paper we consider the heat equation with a strongly singular potential and show that it has a very weak solution. Our analysis is devoted to general hypoelliptic operators…
Liouville theorems for Kirchhoff-type hypoelliptic Partial Differential Equations and systems. I. Heisenberg group
Aidyn Kassymov, Michael Ruzhansky, Niyaz Tokmagambetov +1
In this paper, we show the nonexistence results for the Kirchhoff elliptic, parabolic, and hyperbolic type equations on the Heisenberg groups. Also, the pseudo-parabolic and pseudo…
Fractional Schrödinger equations with singular potentials of higher order. II: Hypoelliptic case
M. Chatzakou, M. Ruzhansky, N. Tokmagambetov
In this paper we consider the space-fractional Schrödinger equation with a singular potential for a wide class of fractional hypoelliptic operators. Such analysis can be convenient…
Fractional Klein-Gordon equation with singular mass. II: Hypoelliptic case
M. Chatzakou, Michael Ruzhansky, Niyaz Tokmagambetov
In this paper we consider a fractional wave equation for hypoelliptic operators with a singular mass term depending on the spacial variable and prove that it has a very weak soluti…
Expansion of traces and Dixmier traceability for global pseudo-differential operators on manifolds with boundary
Duván Cardona, Vishvesh Kumar, Michael Ruzhansky +1
Given a smooth manifold (with or without boundary), in this paper we study the regularisation of traces for the global pseudo-differential calculus in the context of non-harmon…
Global Functional calculus, lower/upper bounds and evolution equations on manifolds with boundary
Duván Cardona, Vishvesh Kumar, Michael Ruzhansky +1
Given a smooth manifold (with or without boundary), in this paper we establish a global functional calculus (without the standard assumption that the operators are classical ps…
Sobolev, Hardy, Gagliardo-Nirenberg and Caffarelli-Kohn-Nirenberg type inequalities for some fractional derivatives
Aidyn Kassymov, Michael Ruzhansky, Niyaz Tokmagambetov +1
In this paper we show different inequalities for fractional order differential operators. In particular, the Sobolev, Hardy, Gagliardo-Nirenberg and Caffarelli-Kohn-Nirenberg type…
A parallel hybrid implementation of the 2D acoustic wave equation
Arshyn Altybay, Michael Ruzhansky, Niyaz Tokmagambetov
In this paper, we propose a hybrid parallel programming approach for a numerical solution of a two-dimensional acoustic wave equation using an implicit difference scheme for a sing…
Tsunami propagation for singular topographies
Arshyn Altybay, Michael Ruzhansky, Mohammed Elamine Sebih +1
We consider a tsunami wave equation with singular coefficients and prove that it has a very weak solution. Moreover, we show the uniqueness results and consistency theorem of the v…
Direct and Inverse problems for time-fractional pseudo-parabolic equations
Michael Ruzhansky, Daurenbek Serikbaev, Niyaz Tokmagambetov +1
The purpose of this paper is to establish the solvability results to direct and inverse problems for time-fractional pseudo-parabolic equations with the self-adjoint operators. We…
- boundedness of pseudo-differential operators on smooth manifolds and its applications to nonlinear equations
Duván Cardona Sánchez, Vishvesh Kumar, Michael Ruzhansky +1
In this paper we study the boundedness of global pseudo-differential operators on smooth manifolds. By using the notion of global symbol we extend a classical condition of Hörmande…