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...

Previous work [51] showed how to solve time-fractional diffusion equations by particle tracking. This paper extends the method to the case where the order of the fractional time derivative is greater than one. A subordination approach treats the fractional time derivative as a random time change of the corresponding Cauchy problem, with a first derivative in time. One novel feature of the time ...

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...

In this paper, we consider the inverse problem for identifying initial value of time–space fractional nonlinear diffusion equation. The uniqueness solution is proved by taking fixed point theorem Banach compression, and ill-posedness analyzed through exact solution. quasi-boundary regularization method chosen to solve ill-posed problem, error estimate between given. Moreover, several numerical ...

The article presents a method for solving the inverse problem of two-dimensional anomalous diffusion equation with Riemann–Liouville fractional-order derivative. In first part present study, authors numerical solution direct problem. For this purpose, differential scheme was developed based on alternating direction implicit method. presented accompanied by examples illustrating its accuracy. se...

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...

The least-squares linear inverse estimation problem for random fields is studied in a fractional generalized framework. First, the second-order regularity properties of the random fields involved in this problem are analysed in terms of the fractional Sobolev norms. Second, the incorporation of prior information in the form of a fractional stochastic model, with covariance operator bicontinuous...

We address in this paper the problem of modifying both profits and costs of a fractional knapsack problem optimally such that a prespectified solution becomes an optimal solution with prespect to new parameters. This problem is called the inverse fractional knapsack problem. Concerning the l1-norm, we first prove that the problem is NP -hard. The problem can be however solved in quadratic time ...

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.
 As result, could be determined with high precision. Illustrative examples shows that retrieved and solution problem are a...