Let E ⊂ R n+1 , n ≥ 2, be an Ahlfors-David regular set of dimension n.We show that the weak-A ∞ property harmonic measure, for open Ω := \

Fractional (nonlocal) diffusion equations replace the integer-order derivatives in space and time by their fractional-order analogs they are used to model anomalous diffusion, especially physics. In this paper, we study a backward problem for an inhomogeneous time-fractional equation with variable coefficients general bounded domain. Such is of practically great importance because often do not know initial density substance, but can observe at positive moment. The ill-posed propose...

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In this paper, we study the parabolic problem associated with non-local conditions, Caputo-Fabrizio derivative.Equations on sphere have many important applications in physics, phenomena, and oceanography.The main motivation for us to boundary value problems comes from two reasons: first reason is that current major interest several application areas.The second approximation terminal problem.With some given data, prove has only solution cases.In case = 0, a local solution.In > then global...

Abstract In this work, we study the problem to identify an unknown source term for Atangana–Baleanu fractional derivative. general, is severely ill-posed in sense of Hadamard. We have applied generalized Tikhonov method regularize instable solution problem. theoretical result, show error estimate between regularized and exact solutions with a priori parameter choice rules. present numerical example illustrate result. According example, that proposed regularization converged.

In this article, we study an inverse problem with inhomogeneous source to determine initial data from the time fractional diffusion equation. general, is ill‐posed in sense of Hadamard, so quasi‐boundary value method proposed solve problem. theoretical results, propose a priori and posteriori parameter choice rules analyze them. Finally, two numerical results one‐dimensional two‐dimensional case show evidence used regularization method.

Abstract In this article, we first study the inverse source problem for parabolic with memory term. We show that our is ill-posed in sense of Hadamard. Then, construct convergence result when parameter tends to zero. also investigate regularized solution using Fourier truncation method. The error estimate between and exact obtained.

In this paper, we investigate an equation of nonlinear fractional diffusion with the derivative Riemann–Liouville. Firstly, determine global existence and uniqueness mild solution. Next, under some assumptions on input data, discuss continuity regard to order for time. Our key idea is combine theories Mittag–Leffler functions Banach fixed‐point theorem. Finally, present examples test proposed theory.

This paper presents a numerical technique to approximate the Rayleigh–Stokes model for generalised Maxwell fluid formulated in Riemann–Liouville sense. The proposed method consists of two stages. First, time discretization problem is accomplished by using finite difference. Second, space obtained means predictor–corrector method. unconditional stability result and convergence analysis are analysed theoretically. Numerical examples provided verify feasibility accuracy

In this paper, we study an inverse source problem for the Rayleigh–Stokes a generalized second-grade fluid with fractional derivative model. The is severely ill-posed in sense of Hadamard. To regularize unstable solution, apply Tikhonov method regularization solution and obtain priori error estimate between exact regularized solutions. We also propose methods both posteriori parameter choice rules. addition, verify proposed by numerical experiments to errors

Abstract In this study, we study an inverse source problem for the time-fractional diffusion equation, where final data $t = T$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>t</mml:mi><mml:mo>=</mml:mo><mml:mi>T</mml:mi></mml:math> are given. We show that our is ill-posed in sense of Hadamard. Applying a truncation method, give regularized solution. Finally, convergence estimates under priori and posteriori parameter choice rules proved.

In this study, we study an inverse source problem of the bi-parabolic equation. The is severely non-well-posed in sense Hadamard, called well-posed if it satisfies three conditions, such as existence, uniqueness, and stability solution. If one these properties not satisfied, non (ill-posed). According to our research experience, sought solution are most often violated. Therefore, a regularization method required. Here, apply Modified Quasi Boundary Method deal with problem. Base on method,...

In this article, we deal with the inverse problem of identifying unknown source time-fractional diffusion equation in a cylinder by A fractional Landweber method. This is ill-posed. Therefore, regularization required. The main result article error between sought solution and its regularized under selection priori parameter choice rule.

The Caputo-Hadamard derivative was used to investigate the problem of functional recovery in this study. This is ill-posed, we propose a novel Quasi-reversibility for reconstructing sought function and show that regularization solution depends on space. After that, convergence rates are established under priori posterior choice rules parameters, respectively.