A modified quasi-boundary value method for a backward problem for the inhomogeneous time conformable fractional heat equation in a cylinder. Issue 9 (2nd September 2021)

• Record Type: Journal Article
• Authors: Yang, Shuping; Xue, Xuemin; Xiong, Xiangtuan
• Is Part Of: Inverse problems in science and engineering. Volume 29:Issue 9(2021)
• Page Start: 1323
• Page End: 1342
• Publication Date: 2021-09-02
• Subjects: Backward heat problem -- quasi-boundary value method -- conformable derivative -- error estimate; 35R25 -- 35R30 -- 65J20 -- 65M30; Engineering mathematics -- Periodicals; Inverse problems (Differential equations) -- Periodicals; 620.001515357
• DOI: 10.1080/17415977.2020.1849179
• Languages: English
• ISSNs: 1741-5977

Abstract

ABSTRACT: The time conformable heat equation is a generalization of classical heat equation involved local and limit-based derivative, which is called conformable fractional derivative. In this paper, we study a backward problem for the time conformable fractional heat equation defined in cylindrical coordinates for the axis-symmetric case which is a severely ill-posed problem. By using a modified quasi-boundary value method, the problem is regularized and some new error estimates are obtained. The numerical experiment shows that the method is feasible and effective.