In this paper, the inverse problem for identifying initial value of a time fractional nonhomogeneous diffusion equation in columnar symmetric region is studied. This an ill-posed problem, i.e., solution does not depend continuously on data. The Tikhonov regularization method applied to solve and obtain solution. error estimations between exact are also obtained under priori posteriori parameter...

Related DatabasesWeb of Science You must be logged in with an active subscription to view this.Article DataHistorySubmitted: 13 August 2020Accepted: 08 December 2020Published online: January 2021Keywordsfractional partial differential equations, inverse problems, Runge approximation propertyAMS Subject Headings35R11, 35R30Publication DataISSN (print): 0036-1410ISSN (online): 1095-7154Publisher:...

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 ...

Exact and approximate solutions of the fractional diffusion equation for an assembly of fixed-axis dipoles are derived for anomalous noninertial rotational diffusion in a double-well potential. It is shown that knowledge of three time constants characterizing the normal diffusion, viz., the integral relaxation time, the effective relaxation time, and the inverse of the smallest eigenvalue of th...

Based on the recently introduced fractional Taylor’s formula, a fractional heat conduction constitutive equation is formulated by expanding the single-phase lag model using the fractional Taylor’s formula. Combining with the energy balance equation, the derived fractional heat conduction equation has been shown to be capable of modeling diffusion-to-Thermal wave behavior of heat propagation by ...

Abstract We consider the Cauchy-type problem associated to time fractional partial differential equation: $$\begin{aligned} {\left\{ \begin{array}{ll} \partial _t u+\partial _t^{\beta }u-\varDelta u=g(t,x), &amp;{} t&gt;0, \ x\in {\mathbb {R}}^n \\ u(0,x)=u_0(x), \end{array}\right. } \end{aligned}$$ <mml...

We consider initial boundary value problems for one-dimensional diffusion equation with time-fractional derivative of order α∈(0,1) which are subject to non-zero Neumann conditions. prove the uniqueness an inverse coefficient problem determining a spatially varying potential and by Dirichlet data at one end point spatial interval. The imposed conditions required be within correct Sobolev space ...

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 ...