An identification problem involving fractional differential variational inequalities

Abstract

We study the solvability and stability for the problem of identifying parameter in a class of fractional differential variational inequalities. Our approach is based on a regularity analysis for fractional diffusion equations and fixed point techniques.

Asymptotically periodic solutions for fractional differential variational inequalities

“…For various motivations, differential variational inequalities (DVIs) in Euclidean spaces and general Banach spaces have been studied extensively recently; e.g. Pang and Stewart [28,31], Avgerinos and Papageorgiou [7], Gwinner [15,16], Liu Zhenhai et al [24,23,22,21], Anh [2,3], Ke et al [5,6,20] and references cited therein. Built on dynamical systems associated with variational inequalities, differential variational inequalities open up a broad paradigm for the enhanced modeling of complex real-world engineering systems, such as mechanical impact problems, electrical circuits with ideal diodes, Coulomb friction problems for contacting bodies, economical dynamics and hybrid engineering systems with variable structures.…”

Regularity theory for fractional reaction–subdiffusion equation and application to inverse problem

“…This question arises in many aspects of mathematical analysis, for example, in establishing various discretization schemes in time to finding the approximation solutions of such these equations (see, e.g., previous studies [24][25][26][27] ) or in studying the existence and stability for some kinds of inverse prob-lems. 8,[28][29][30][31][32][33][34] Up to date, there are many noticeable results in the literature dealing with the existence of smooth solutions for tFrPDEs; see previous studies 6,[35][36][37][38] and the bibliographies quoted therein.…”

Source identification problems for abstract semilinear nonlocal differential equations

“…They also proved several general uniqueness results in simultaneously recovering both the medium parameter and the internal source by the corresponding exterior measurements in [3]. The problem of identifying parameter in a class of fractional differential variational inequalities based on a regularity analysis for fractional diffusion equations under the measurement condition was studied in [18]. With regard to the termial time problem for Caputo time-fractional, the stability and the regularity of solutions as well as numerical implementations have been studied extensively in [7,9,8] by Dinh Nho Hào's research group.…”