Oct 2026· Mathematics· Vol 14, pp. 3641· 0 citations· 40 references
Abstract
For a one-dimensional time-fractional diffusion-wave equation, we investigate joint recovery of its fractional order and the initial velocity from measurements taken at one interior point. Uniqueness is proved through analytic continuation, Laplace transforms, an integral mean value theorem, and Mittag-Leffler function properties. The ill-posed reconstruction is regularized in a Bayesian setting using the iterative regularizing ensemble Kalman method. The posterior measure is shown to exist and to depend stably on the data; its numerical approximation converges under an assumed error bound for the forward solver. The resulting method is assessed in three numerical tests, which illustrate its effectiveness as well as its stability.
We consider a inverse problem for a hyperbolic equation. The objective is to simultaneous recover both the spatially varying coefficient, whose square root represents the wave speed, and the initial displacement from a single pair of Dirichlet-Neumann Cauchy data. By introducing a suitable transformation and differenti...
We establish the existence and uniqueness of solutions to a $(1+1)$-dimensional fractional stochastic Burgers-type equation featuring a Caputo fractional time derivative, a fractional Laplacian, and space-time white noise forcing modified by a Riemann-Liouville fractional integral. From a physical perspective, equation...
We study the inverse problem of identifying an unknown time-dependent source in a linear time-fractional diffusion equation, where the time derivative is taken in the Caputo sense of fractional order α . The problem is ill-posed in the sense of Hadamard: the solution does not depend continuously on the measured data, s...
Ouarda Tabrha, Naceur Rahmani, C. Latrous· Gulf Journal of Mathematics· 0 citations
This paper presents an efficient localized meshless method for solving the nonlinear time-fractional Schrödinger equation and the time-fractional Schrödinger–Poisson system. The proposed approach consists of two main steps. First, the Caputo time-fractional derivative is approximated using the L1 formula, which has an...
O. Nikan, Zakieh Avazzadeh· Mathematics· 0 citations
This paper introduces an explicit finite-difference scheme (FDS) for time–space fractional-order (FO) advection equations whose temporal and spatial derivatives have different FOs. The discretization is constructed from a FO Taylor expansion and produces a forward-Euler–type approximation of Caputo derivatives. We prov...
Amer Dababneh, H. Al-Zoubi· International Journal of Ope...· 0 citations
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