Inverse coefficient problems for a time-fractional wave equation with the generalized Riemann-Liouville time derivative

Author:

Turdiev H. H.1

Affiliation:

1. Bukhara branch of the institute of Mathematics named after V.I. Romanovskiy at the Academy of sciences of the Republic of Uzbekistan; Bukhara State University

Abstract

This paper considers the inverse problem of determining the time-dependent coeffiicient in the fractional wave equation with Hilfer derivative. In this case, the direct problem is initial-boundary value problem for this equation with Cauchy type initial and nonlocal boundary conditions. As overdetermination condition nonlocal integral condition with respect to direct problem solution is given. By the Fourier method, this problem is reduced to equivalent integral equations. Then, using the Mittag-Leffler function and the generalized singular Gronwall inequality, we get apriori estimate for solution via unknown coefficient which we will need to study of the inverse problem. The inverse problem is reduced to the equivalent integral of equation of Volterra type. The principle of contracted mapping is used to solve this equation. Local existence and global uniqueness results are proved.

Publisher

Kazan Federal University

Subject

General Earth and Planetary Sciences,General Environmental Science

Reference28 articles.

1. Hilfer R. Applications of Fractional Calculus in Physics (World Scientific, Singapore, 2000).

2. Podlubny I. Fractional Differential Equations. In: Mathematics in Science and Engineering, V. 198 (Academic Press, New York, 1999).

3. Hilfer R., Luchko Y., Tomovski Z. Operational method for the solution of fractional differential equations with generalized Riemann Liouville fractional derivatives, Fract. Calc. Appl. Anal. 12 (3), 299-318 (2009).

4. Kilbas A.A., Srivastava H.M., Trujillo J.J. Theory and Application of Fractional Differential Equations (Elsevier, Amsterdam, 2006).

5. Vinagre B.M., Podlubny I., Hernandez A., Feliu V. Some Approximations of Fractional Order Operators Used in Control Theory and Applications, Fract. Calc. Appl. Anal. 3 (3), 231-248 (2000).

Cited by 3 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

同舟云学术

1.学者识别学者识别

2.学术分析学术分析

3.人才评估人才评估

"同舟云学术"是以全球学者为主线,采集、加工和组织学术论文而形成的新型学术文献查询和分析系统,可以对全球学者进行文献检索和人才价值评估。用户可以通过关注某些学科领域的顶尖人物而持续追踪该领域的学科进展和研究前沿。经过近期的数据扩容,当前同舟云学术共收录了国内外主流学术期刊6万余种,收集的期刊论文及会议论文总量共计约1.5亿篇,并以每天添加12000余篇中外论文的速度递增。我们也可以为用户提供个性化、定制化的学者数据。欢迎来电咨询!咨询电话:010-8811{复制后删除}0370

www.globalauthorid.com

TOP

Copyright © 2019-2024 北京同舟云网络信息技术有限公司
京公网安备11010802033243号  京ICP备18003416号-3