Abstract In this work, we study an initial value problem for a system of nonlinear parabolic pseudo equations with Caputo fractional derivative. Here, discuss the continuity which is related to order To overcome some difficulties problem, need evaluate relevant quantities Mittag-Leffler function by constants independent derivative order. Moreover, present example illustrate theory.

In this paper, we deal with the backward problem of determining initial condition for Rayleigh‐Stokes where data are given at a fixed time. The has many applications in some non‐Newtonian fluids. We give regularity properties solution to problem.

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 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 general filter method constructing regularized and convergence rate also has been investigated.

Abstract In this paper, we consider an inverse problem of identifying the source term for a generalization time-fractional diffusion equation, where regularized hyper-Bessel operator is used instead time derivative. First, investigate existence our term; conditional stability also investigated. Then, show that backward ill-posed; fractional Landweber method and Tikhonov are to deal with problem, solution obtained. We present convergence rates exact by using priori regularization parameter...

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.

<p style='text-indent:20px;'>Solutions of a direct problem for stochastic pseudo-parabolic equation with fractional Caputo derivative are investigated, in which the non-linear space-time-noise is assumed to satisfy distinct Lipshitz conditions including globally and locally assumptions. The main aim this work establish some existence, uniqueness, regularity, continuity results mild solutions.</p>

In this paper, we consider a degenerate parabolic equation associated with Caputo derivative. Our problem is studied in the unbounded domain and nonlocal initial condition. Under some suitable conditions of input data, show local existence mild solution. Then continuation We also claim maximal The main analysis current paper based on estimations resolvent theory combined many complex valuations solutions operators Banach spaces.

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

We investigate a backward problem for the Rayleigh‐Stokes problem, which aims to determine initial status of some physical field such as temperature slow diffusion from its present measurement data. This is well‐known be ill‐posed because rapid decay forward process. construct regularized solution using filter regularization method in Gaussian random noise. Under priori assumptions on exact solution, we establish expectation between and L 2 H m norms.

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,...

Abstract In this paper, we consider an inverse source problem for the time-space-fractional diffusion equation. Here, in sense of Hadamard, prove that is severely ill-posed. By applying quasi-reversibility regularization method, propose by method to solve (1.1). After that, give error estimate between sought solution and regularized under a prior parameter choice rule posterior rule, respectively. Finally, present numerical example find proposed works well.

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.

Summary Data from the 4172 women aged 15–49 interviewed in 1988 Vietnamese Demographic and Health Survey were used to examine age at marriage, marriage first birth intervals birth. Differences between urban rural areas, northern southern provinces by education of analysed. The majority had their before 20, but with secondary a significantly higher than those little or no education, north south. Rural married younger ages education; these effects confirmed subsample women. Women areas shorter...

Abstract In this paper, we consider the initial inverse problem for a diffusion equation with conformable derivative in general bounded domain. We show that backward is ill-posed, and propose regularizing scheme using fractional Landweber regularization method. also present error estimates between regularized solution exact two parameter choice rules.

In this paper, we consider a pseudo‐parabolic equation with the Caputo fractional derivative. We study existence and uniqueness of class mild solutions these equations. For nonlinear problem, first investigate global solution under initial data u 0 ∈ L 2 . case q , ≠ 2, obtain local result. Our main tool here is using fundamental tools, namely, Banach fixed point theorem Sobolev embeddings. addition, give an example to illustrate effectiveness method has been proposed.

Abstract In this work, we consider a fractional diffusion equation with nonlocal integral condition. We give form of the mild solution under expression Fourier series which contains some Mittag-Leffler functions. present two new results. Firstly, show well-posedness and regularity for our problem. Secondly, ill-posedness problem in sense Hadamard. Using truncation method, construct regularized convergence rate between exact solutions.

In this article, we consider an inverse problem to determine unknown source term in a space-time-fractional diffusion equation. The problems are often ill-posed. By example, show that is NOT well-posed the Hadamard sense, i.e., does not satisfy last condition-the solution’s behavior changes continuously with input data. It leads having regularization model for problem. We use Tikhonov method solve theoretical results, also propose priori and posteriori parameter choice rules analyze them.

Abstract In this paper, we consider a time-fractional backward problem for the fractional Rayleigh–Stokes equation in general bounded domain. We propose Landweber regularization method solving problem. Error estimates between regularized solution and sought are also obtained under some choice rules both a-priori a-posterior parameters.

This article is concerned with a forward problem for the following sub-diffusion equation driven by standard Brownian motion&#x0D; \begin{align*} &#x0D; \left( ^{\mathcal C} \partial^\gamma_t + A \right) u(t) = f(t) B(t) \dot{W}(t), \quad t\in J:=(0,T),&#x0D; \end{align*} where $^{\mathcal \partial^\gamma_t$ conformable derivative, $\gamma \in (\frac{1}{2},1].$ Under some flexible assumptions on $f,B$ and initial data, we investigate existence, regularity, continuity of solution two spaces...

Abstract This article is devoted to the study of source function for Caputo–Fabrizio time fractional diffusion equation. new definition derivative has no singularity. In other words, a smooth kernel. Here, we investigate existence term. Through an example, show that this problem ill-posed (in sense Hadamard), and Landweber method modified quasi-boundary value are used deal with inverse regularized solution also obtained. The convergence estimates addressed exact by using priori...