广义时间分数扩散方程的逆源问题

Pub Date : 2022-03-01 DOI:10.32523/2306-6172-2022-10-1-26-39

R. Faizi, R. Atmania

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引用次数: 0

摘要

摘要本文研究了在非局部边界和积分超定条件下，广义时间分数扩散方程的时间相关系数的反问题。利用双正交函数系统和分式微积分，在解的表达式的基础上，通过一种方法，得到了所考虑的反问题解的存在性和唯一性。此外，我们展示了它对数据的持续依赖性。最后，通过两个算例对所得结果进行了说明。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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AN INVERSE SOURCE PROBLEM FOR A GENERALIZED TIME FRACTIONAL DIFFUSION EQUATION

Abstract This paper is devoted to the study of the inverse problem of finding the time- dependent coefficient of a generalized time fractional diffusion equation, in the case of non- local boundary and integral overdetermination conditions. The existence and uniqueness of the solution of the considered inverse problem are obtained by a method based on the expan- sion of the solution by using a bi-orthogonal system of functions and the fractional calculus. Moreover, we show its continuous dependence on the data. At the end, two examples are presented to illustrate the obtained results.

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