38 citations · 40 across the 9 of their papers we have counts for
10 papers
Fractional-Diffraction-Optics Cauchy Problem: Resolvent-Function Solution of the Matrix Integral Equation
Murat O. Mamchuev, Felix N. Chukhovskii
The fractional diffraction optics theory has been elaborated using the Green function technique. The optics-fractional equation describing the diffraction X-ray scattering by imper…
Towards to solution of the fractional Takagi-Taupin equations. The Green function method
Murat O. Mamchuev, Felix N. Chukhovskii
Developing the comprehensive theory of the X-ray diffraction by distorted crystals remains to be topical of the mathematical physics. Up to now, the X-ray diffraction theory ground…
Cauchy Problem for a Linear System of Ordinary Differential Equations of the Fractional Order
Murat Osmanovich Mamchuev
The paper investigates the initial problem for a linear system of ordinary differential equations with the fractional differentiation operator Dzhrbashyan -- Nersesyan with constan…
New estimate for the multinomial Mittag-Leffler function
Murat Mamchuev
In this paper, a new estimate is obtained for the multinomial Mittag-Leffler function. This function was introduced by Yuri Luchko and Rudolfo Gorenflo as the fundamental solution…
Boundary value problem for a multidimensional system of equation with Riemann-Liouville derivatives
M. O. Mamchuev
In the paper boundary-value problem for a multidimensional system of partial differential equations with fractional derivatives in Riemann-Liouville sense with constant coefficient…
Necessary non-local conditions for a time-fractional diffusion-wave equation
M. O. Mamchuev
In this paper the time-fractional diffusion-wave equation with Riemman-Liouville fractional derivative is studied. The integral operators with the Wright function in the kernel, as…
Non-local initial problem for second order time-fractional and space-singular equation
Erkinjon Karimov, Murat Mamchuev, Michael Ruzhansky
In this work, we consider an initial problem for second order partial differential equations with Caputo fractional derivatives in the time-variable and Bessel operator in the spac…
On boundary-value problems for a partial differential equation with Caputo and Bessel operators
Praveen Agarwal, Erkinjon Karimov, Murat Mamchuev +1
In this work, we investigate a unique solvability of a direct and inverse source problem for a time-fractional partial differential equation with the Caputo and Bessel operators. U…
Boundary value problem for the time-fractional telegraph equation with Caputo derivatives
M. O. Mamchuev
In this paper the Green formula for the operator of fractional differentiation in Caputo sense is proved. By using this formula the integral representation of all regular in a rect…
Solutions of the main boundary value problems for the time-fractional telegraph equation by the Green function method
Murat O. Mamchuev
The inhomogenous time-fractional telegraph equation with Caputo derevatives with constant coefficients is considered. For considered equation the general representation of regular…