In this contribution, we investigate an inverse source problem for a fractional diffusion and wave equation with the Caputo derivative of space-dependent variable order. More specifically, discuss uniqueness solution when reconstructing from time-averaged measurement, or final in time measurement. Weakly singular solutions are included class admissible solutions. The obtained results also valid...

In this study, an inverse source problem for a one-dimensional timefractional diffusion equation is considered. An existence theorem based on the minimization of an error functional between the output data and the additional data is proved. Then it is showed that the unknown source function can be determined uniquely by an additional data u(0, t), 0 ≤ t ≤ T using an auxiliary uniqueness result ...

A fractional normal inverse Gaussian (FNIG) process is a fractional Brownian motion subordinated to an inverse Gaussian process. This paper shows how the FNIG process emerges naturally as the limit of a random walk with correlated jumps separated by i.i.d. waiting times. Similarly, we show that the NIG process, a Brownian motion subordinated to an inverse Gaussian process, is the limit of a ran...

In this paper, two inverse problems for the fractional diffusion-wave equation that use final data are considered. The first problem consists in determination of time-dependent source terms. Uniqueness is established under an assumption given space-dependent factors these terms “sufficiently different”. proof uses asymptotical properties Mittag–Leffler functions. second problem, aim to reconstr...

We study a porous medium equation with right hand side. The operator has nonlocal diffusion effects given by an inverse fractional Laplacian operator. The derivative in time is also fractional of Caputo-type and which takes into account “memory”. The precise model is D t u− div(u(−∆)−σu) = f, 0 < σ < 1/2. We pose the problem over {t ∈ R+, x ∈ Rn} with nonnegative initial data u(0, x) ≥ 0 as wel...

n this paper, at first the  concept of caputo fractionalderivative is generalized on time scales. then the fractional orderdifferential equations are introduced on time scales. finally,sufficient and necessary conditions are presented for the existenceand uniqueness of solution of initial valueproblem including fractional order differential equations.

The goal of this research is to reveal the unknown time dependent diffusion coefficient in space-time fractional differential equations by means Taylor series method. Unlike most methods used inverse problems, using no over-measured data a substantial advantage method.&#x0D; As result, could be determined with high precision. Illustrative examples shows that retrieved and solution problem are a...

In this paper, we consider the backward problem for a time fractional diffusion-wave equation in cylinder. The ill-posedness and conditional stability of inverse are proved. Based on generalized quasi-boundary value regularization method, propose an iterative method to deal with problem, has higher convergence rate. rates regularized solution under priori parameter choice rule posteriori obtain...