Fractional Dzherbashian-Nersesian operator is considered and three famous fractional order derivatives named after Riemann-Liouville, Caputo Hilfer are shown to be special cases of the earlier one. The expression for Laplace transform constructed. Inverse problems recovering space dependent time source terms a diffusion equation with involution involving considered. results on existence uniquen...

In this paper, we consider the numerical inverse Laplace transform for distributed order time-fractional equations, where a discontinuous Galerkin scheme is used to discretize problem in space. The success of Talbot’s approach computation depends critically on problem’s spectral properties and present method numerically enclose spectrum compute resolvent estimates independent size. new results ...

This article considers an inverse problem of time fractional parabolic partial differential equations with the nonlocal boundary condition. Dirichlet-measured output data are used to distinguish unknown coefficient. A finite difference scheme is constructed and a numerical approximation made. Examples experiments, such as man-made noise, provided show stability efficiency this method.

This article is concerned with two inverse problems on determining moving source profile functions in evolution equations a derivative order $\alpha\in(0,2]$ time. In the first problem, sources are supposed to move along known straight lines, and we suitably choose partial interior observation data finite Reducing determination of initial values, prove unique one profiles for $0<\alpha\le1$ $1<...

Journal of Applied Mathematics and Computational Mechanics, Prace Naukowe Instytutu Matematyki i Informatyki, Politechnika Częstochowska, Scientific Research the Institute Computer Science, Czestochowa University Technology

This paper deals with an inverse problem for identifying multiparameters in 1D space fractional advection dispersion equation FADE on a finite domain with final observations. The parameters to be identified are the fractional order, the diffusion coefficient, and the average velocity in the FADE. The forward problem is solved by a finite difference scheme, and then an optimal perturbation regul...

This paper is focused on the inverse problem of identifying space-dependent source function and initial value time fractional nonhomogeneous diffusion-wave equation from noisy final measured data in a multi-dimensional case. A mollification regularization method based bilateral exponential kernel presented to solve ill-posedness for first time. Error estimates are obtained with an priori strate...