Simultaneous determination of a Source Term and diffusion concentration for a Multi-Term Space-Time fractional diffusion equation

IF 1.6 3区 数学 Q1 MATHEMATICS
S. Malik, Asim Ilyas, Arifa Samreen
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引用次数: 9

Abstract

An inverse problem of determining a time dependent source term along with diffusion/temperature concentration from a non-local over-specified condition for a space-time fractional diffusion equation is considered. The space-time fractional diffusion equation involve Caputo fractional derivative in space and Hilfer fractional derivatives in time of different orders between 0 and 1. Under certain conditions on the given data we proved that the inverse problem is locally well-posed in the sense of Hadamard. Our method of proof based on eigenfunction expansion for which the eigenfunctions (which are Mittag-Leffler functions) of fractional order spectral problem and its adjoint problem are considered. Several properties of multinomial Mittag-Leffler functions are proved.
多项时空分数扩散方程源项和扩散浓度的同时确定
考虑了时空分数阶扩散方程在非局部过指定条件下确定源项随扩散/温度浓度随时间变化的反问题。时空分数扩散方程包含空间上的Caputo分数阶导数和时间上的Hilfer分数阶导数,其阶数在0 ~ 1之间。在给定数据的一定条件下,证明了逆问题在Hadamard意义上是局部适定的。考虑分数阶谱问题及其伴随问题的特征函数(即Mittag-Leffler函数),提出了基于特征函数展开的证明方法。证明了多项式Mittag-Leffler函数的几个性质。
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来源期刊
CiteScore
2.80
自引率
5.60%
发文量
28
审稿时长
4.5 months
期刊介绍: Mathematical Modelling and Analysis publishes original research on all areas of mathematical modelling and analysis.
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