Simultaneous determination of a source term and diffusion concentration for a multi-term space-time fractional diffusion equation

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 s...

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Published inMathematical modelling and analysis Vol. 26; no. 3; pp. 411 - 431
Main Authors Malik, Salman A., Ilyas, Asim, Samreen, Arifa
Format Journal Article
LanguageEnglish
Published Vilnius Vilnius Gediminas Technical University 13.07.2021
Subjects
bi-orthogonal system of functions
Diffusion
Eigenvectors
fractional derivative
Functional equations
Functions
inverse problem
Inverse problems
Mathematical research
multinomial mittag-leffler function
Space and time
Spacetime
Time dependence
Pakistan
inverse problem
fractional derivative
Bi-orthogonal system of functions
multinomial Mittag-Leffler function
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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.
AbstractList 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.
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. Keywords: inverse problem, fractional derivative, Bi-orthogonal system of functions, multinomial Mittag-Leffler function. AMS Subject Classification: 26A33; 35R30; 35P10; 44A10; 33E12.
Audience Academic
Author Malik, Salman A.
Samreen, Arifa
Ilyas, Asim
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  surname: Samreen
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  organization: Department of Mathematics, COMSATS University Islamabad, Park Road, Chak Shahzad Islamabad, Pakistan
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Snippet An inverse problem of determining a time dependent source term along with diffusion/temperature concentration from a non-local over-specified condition for a...
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SubjectTerms bi-orthogonal system of functions
Diffusion
Eigenvectors
fractional derivative
Functional equations
Functions
inverse problem
Inverse problems
Mathematical research
multinomial mittag-leffler function
Space and time
Spacetime
Time dependence
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Title Simultaneous determination of a source term and diffusion concentration for a multi-term space-time fractional diffusion equation
URI https://journals.vilniustech.lt/index.php/MMA/article/view/11911
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Volume 26
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