On the inverse problems for a family of integro-differential equations

K Suhaib, A Ilyas, SA Malik - Mathematical Modelling and Analysis, 2023 - jest.vgtu.lt
An integro-differential equation involving arbitrary kernel in time variable with a family of non-
local boundary condition has been considered. Two inverse source problems for integro …

Solvability of mixed problems for a fourth-order equation with involution and fractional derivative

M Kirane, AA Sarsenbi - Fractal and Fractional, 2023 - mdpi.com
In the present work, two-dimensional mixed problems with the Caputo fractional order
differential operator are studied using the Fourier method of separation of variables. The …

Recovering source term and temperature distribution for nonlocal heat equation

A Ilyas, SA Malik, S Saif - Applied Mathematics and Computation, 2023 - Elsevier
We consider two problems of recovering the source terms along with heat concentration for
a time fractional heat equation involving the so-called m th level fractional derivative …

An inverse source problem for anomalous diffusion equation with generalized fractional derivative in time

A Ilyas, SA Malik - Acta Applicandae Mathematicae, 2022 - Springer
The inverse problem of recovering a source term along with diffusion concentration for a
generalized diffusion equation has been considered. The so-called 2nd level fractional …

Identifying diffusion concentration and source term for anomalous diffusion equation

A Ilyas, SA Malik, K Suhaib - Reports on Mathematical Physics, 2024 - Elsevier
We consider an inverse problem for diffusion equation involving fractional Laplacian
operator in space and Hilfer fractional derivatives in time with Dirichlet zero boundary …

Direct and some inverse problems for a generalized diffusion equation with variable coefficients

A Ilyas, SA Malik - Computational and Applied Mathematics, 2024 - Springer
Direct and two inverse problems for a Legendre equation involving integral convolution in
time are studied. The inverse problems are ill-posed in the sense of Hadamard. The …

The inverse problem for the heat equation with reflection of the argument and with a complex coefficient

E Mussirepova, A Sarsenbi, A Sarsenbi - Boundary Value Problems, 2022 - Springer
The paper is devoted to finding a solution and restoring the right-hand side of the heat
equation with reflection of the argument in the second derivative, with a complex-valued …

Inverse coefficient problem for the time‐fractional diffusion equation with Hilfer operator

DK Durdiev - Mathematical Methods in the Applied Sciences, 2023 - Wiley Online Library
In this paper, the inverse problem of determining the time‐dependent reaction–diffusion
coefficient in the Cauchy problem for the time‐fractional diffusion equation with the Hilfer …

Pseudospectral quadrature simulation technique for spatio-temporally parabolic multi-dimensional nonlinear fractional evolution equation

AK Mittal - The Journal of Analysis, 2024 - Springer
The aim of this paper, the author is to introduce the Jacobi pseudospectral quadrature
simulation technique for the multi-dimensional nonlinear fractional evolution equation. We …

An inverse problem for a two‐dimensional diffusion equation with arbitrary memory kernel

S Saif, S Malik - Mathematical Methods in the Applied Sciences, 2023 - Wiley Online Library
An inverse source problem (ISP) of recovering space‐dependent source term along with
diffusion concentration for a two‐dimensional diffusion equation involving integral …