2021
DOI: 10.1007/s11075-021-01210-w
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A solely time-dependent source reconstruction in a multiterm time-fractional order diffusion equation with non-smooth solutions

Abstract: An inverse source problem for non-smooth multiterm time Caputo fractional diffusion with fractional order designed asThe missing solely time dependent source function is reconstructed from an additional integral measurement. The existence, uniqueness and regularity of a weak solution for the inverse source problem is investigated. We design a numerical algorithm based on Rothe's method over graded meshes, derive a priori estimates and prove convergence of iterates towards the exact solution. An essential featu… Show more

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Cited by 9 publications
(2 citation statements)
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“…A survey of the numerical techniques that have been applied to direct and inverse problems with integer or fractional order derivatives indicates a lot of focus in recent days [9][10][11]. A reconstruction of missing sole terms in different styles of time-dependent fractional diffusion problems has been seen in [12,13].…”
Section: Introductionmentioning
confidence: 99%
“…A survey of the numerical techniques that have been applied to direct and inverse problems with integer or fractional order derivatives indicates a lot of focus in recent days [9][10][11]. A reconstruction of missing sole terms in different styles of time-dependent fractional diffusion problems has been seen in [12,13].…”
Section: Introductionmentioning
confidence: 99%
“…The existence of a weak solution was obtained using Rothe's method. Meanwhile, well-posedness results in the same problem for multi-term time-fractional diffusion equations are obtained in [HV22b].…”
Section: Introductionmentioning
confidence: 99%