R. Ashurov

Stability in recovering the order of a time-fractional evolution equation

Ravshan Ashurov, Masahiro Yamamoto

We consider the recovery of the fractional order in a time-fractional evolution equation with a source of the form $p (t) f$ , where the temporal factor $p$ is also unknown but belong…

Uniqueness in determining the temporal source factor and the fractional order with an unknown initial value

Ravshan Ashurov, Masahiro Yamamoto

We consider inverse problems for a time-fractional diffusion equation with a second-order elliptic operator and the homogeneous Dirichlet boundary condition in a bounded domain of…

Uniqueness for an inverse problem of determining order and temporal factor of the source for time-fractional evolution equations

Ravshan Ashurov, Masahiro Yamamoto

This paper addresses the inverse problem of simultaneously recovering the fractional order $α \in (0, 1) \cup (1, 2)$ and the time-dependent source factor $p (t)$ in the Cauchy problem…

Forward and inverse problems for a time-fractional pseudo-parabolic equation with variable coefficients

Ravshan Ashurov, Elbek Husanov

In this work, forward and inverse problems for a time-fractional pseudo-parabolic equation $D_{t}^{ρ} [u (t) + μ A u (t)] + σ (t) A u (t) = r (t) g$ are investigated in a Hilbert space, where $…

The backward problem for a multi-term time-fractional diffusion equation

Ravshan Ashurov, Damir Shamuratov

This paper is devoted to the investigation of the backward problem for a multi-term time-fractional diffusion equation. Backward problems for fractional diffusion equations are typ…

Non-local time problem for the Rayleigh--Stokes type fractional equations

Ravshan Ashurov, Yusuf Fayziyev, Nuriddin Khushvaktov

Despite the growing interest in fractional generalizations of classical fluid dynamics equations, the fractional Rayleigh--Stokes problem has previously been studied almost exclusi…

Inverse problem for a multi-term time-fractional diffusion equation with the Caputo derivatives

Ravshan Ashurov, Damir Shamuratov

This paper investigates an inverse source problem for a multi-term time-fractional diffusion equation with Caputo derivatives. The source term is separable as $f(x)g(t)$, with th…

Inverse problem of determining a time-dependent coefficient in the time-fractional subdiffusion equation

Ravshan Ashurov, Elbek Husanov

This paper explores the forward and inverse problems for a fractional subdiffusion equation characterized by time-dependent diffusion and reaction coefficients. Initially, the forw…

Coefficient Identification Problem with Integral Overdetermination Condition for Diffusion Equations

R. R. Ashurov, O. T. Mukhiddinova

In this paper, we investigate a nonlinear inverse problem aimed at recovering a coefficient $a (t, x)$ , dependent on both time and a subset of spatial variables, in a diffusion equa…

Forward and inverse problems for a mixed-type equation with the Caputo fractional derivative and Dezin-type non-local condition

Ravshan Ashurov, Umida Dusanova, Navbahor Nuraliyeva

This work is dedicated to the study of a mixed-type partial differential equation involving a Caputo fractional derivative in the time domain $t > 0$ and a classical parabolic equa…

A Nonlinear Nonlocal Problem for the Caputo Fractional Subdiffusion Equation

Ravshan Ashurov, Rajapboy Saparboyev, Navbahor Nuraliyeva

In this paper, we study a time-fractional subdiffusion equation with a nonlinear nonlocal initial condition involving the unknown solution at the final time. The considered problem…

Source Identification Problem for a Nonlinear Subdiffusion Equation

R. R. Ashurov, O. T. Mukhiddinova

The work is devoted to the study of the inverse problem of determining the right-hand side of a nonlinear subdiffusion equation with a Caputo derivative with respect to time. Nonli…

Space- and Time-Dependent Source Identification Problem with Integral Overdetermination Condition

R. R. Ashurov, O. T. Mukhiddinova

This paper is devoted to the study of the inverse problem of determining the right-hand side of the subdiffusion equation with the Caputo derivative with respect to time. In our ca…

Space-Time-Dependent Source Identification Problem for a Subdiffusion Equation

R. R. Ashurov, O. T. Mukhiddinova

In this paper, we investigate the inverse problem of determining the right-hand side of a subdiffusion equation with a Caputo time derivative, where the right-hand side depends on…

Monotonicity in the parameter of the Mittag-Leffler function and determining the fractional exponent of the subdiffusion equation

Ravshan Ashurov, Ilyoskhuja Sulaymonov

In this paper, we prove the strict monotonicity in the parameter $ρ$ of the Mittag-Leffler functions $E_{ρ} (- t^{ρ})$ and $t^{ρ - 1} E_{ρ, ρ} (- t^{ρ})$ . Then, these results are applied to solv…

On determining the fractional exponent of the subdiffusion equation

Shavkat Alimov, Ravshan Ashurov

Determining the unknown order of the fractional derivative in differential equations simulating various processes is an important task of modern applied mathematics. In the last de…

Inverse source problem for the space-time fractional parabolic equation on a metric star graph with an integral overdetermination condition

R. R. Ashurov, Z. A Sobirov, A. A. Turemuratova

In the present paper, we investigate the initial-boundary value problem for fractional order parabolic equation on a metric star graph in Sobolev spaces. First, we prove the existe…

On fractional parabolic systems of vector order

Ravshan Ashurov, Ilyoskhuja Sulaymonov

The paper considers the Cauchy problem for the system of partial differential equations of fractional order $D_{t}^{B} U (t, x) + A (D) U (t, x) = H (t, x)$ . Here $U$ …

On the non-local problem for Boussinesq type fractional equation

Ravshan Ashurov, Yusuf Fayziev, Muattar Khudoykulova

In recent years, the Boussinesq type fractional partial differential equation has attracted much attentions of researchers for its practical importance. In this paper we study a no…

Determining the order of time and spatial fractional derivatives

Ravshan Ashurov, Ilyoskhuja Sulaymonov

The paper considers the initial-boundary value problem for equation $D_{t}^{ρ} u (x, t) + (- Δ)^{σ} u (x, t) = 0$ , $ρ \in (0, 1)$ , $σ > 0$ , in an N-dimensional domain $Ω$ with a homogeneous Dirichlet…