119 citations · 581 across the 30 of their papers we have counts for
30 papers
The generalized Duhamel principle for fully coupled systems of fractional order
Sabir Umarov
Duhamel's principle reduces the Cauchy problem for an inhomogeneous partial differential equation to the corresponding homogeneous problem. In the fractional-order setting, the cla…
Representations of solutions of time-fractional multi-order systems of differential-operator equations
Sabir Umarov
This paper is devoted to the general theory of systems of time-fractional differential-operator equations. The representation formulas for solutions of systems of ordinary differen…
A non-local problem for the fractional order Rayleigh-Stokes equation
Ravshan Ashurov, Oqila Mukhiddinova, Sabir Umarov
A nonlocal boundary value problem for the fractional version of the well known in fluid dynamics Rayleigh-Stokes equation is studied. Namely, the condition , w…
An inverse problem of determining the orders of systems of fractional pseudo-differential equations
Ravshan Ashurov, Sabir Umarov
As it is known various dynamical processes can be modeled through the systems of time-fractional order pseudo-differential equations. In the modeling process one frequently faces w…
Determination of the order of fractional derivative for subdiffusion equation
Ravshan Ashurov, Sabir Umarov
The identification of the right order of the equation in applied fractional modeling plays an important role. In this paper we consider an inverse problem for determining the order…
Use of the geometric mean as a statistic for the scale of the coupled Gaussian distributions
Kenric P. Nelson, Mark A. Kon, Sabir R. Umarov
The geometric mean is shown to be an appropriate statistic for the scale of a heavy-tailed coupled Gaussian distribution or equivalently the Student's t distribution. The coupled G…