An Inverse Problem of Reconstructing the Unknown Coefficient in a Third Order Time Fractional Pseudoparabolic Equation

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dc.authorid0000-0003-4442-7498
dc.authorid0000-0001-5247-2913
dc.authorid0000-0001-6725-5663
dc.contributor.authorHuntul, Mousa J.
dc.contributor.authorTekin, Ibrahim
dc.contributor.authorIqbal, Muhammad K.
dc.contributor.authorAbbas, Muhammad
dc.date.accessioned2026-01-24T12:26:45Z
dc.date.available2026-01-24T12:26:45Z
dc.date.issued2024
dc.departmentAlanya Alaaddin Keykubat Üniversitesi
dc.description.abstractIn this paper, we have considered the problem of reconstructing the time dependent potential term for the third order time fractional pseudoparabolic equation from an additional data at the left boundary of the space interval. This is very challenging and interesting inverse problem with many important applications in various fields of engineering, mechanics and physics. The existence of unique solution to the problem has been discussed by means of the contraction principle on a small time interval and the unique solvability theorem is proved. The stability results for the inverse problem have also been presented. However, since the governing equation is yet ill-posed (very slight errors in the additional input may cause relatively significant errors in the output potential), the regularization of the solution is needed. Therefore, to get a stable solution, a regularized objective function is to be minimized for retrieval of the unknown coefficient of the potential term. The proposed problem is discretized using the cubic B-spline (CB-spline) collocation technique and has been reshaped as a non-linear least-squares optimization of the Tikhonov regularization function. The stability analysis of the direct numerical scheme has also been presented. The MATLAB subroutine lsqnonlin tool has been used to expedite the numerical computations. Both perturbed data and analytical are inverted and the numerical outcomes for two benchmark test examples are reported and discussed.
dc.identifier.doi10.52846/ami.v51i1.1744
dc.identifier.endpage81
dc.identifier.issn1223-6934
dc.identifier.issn2246-9958
dc.identifier.issue1
dc.identifier.scopus2-s2.0-85199268103
dc.identifier.scopusqualityQ3
dc.identifier.startpage54
dc.identifier.urihttps://doi.org/10.52846/ami.v51i1.1744
dc.identifier.urihttps://hdl.handle.net/20.500.12868/4899
dc.identifier.volume51
dc.identifier.wosWOS:001267819700004
dc.identifier.wosqualityQ2
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.language.isoen
dc.publisherUniv Craiova
dc.relation.ispartofAnnals of The University of Craiova-Mathematics and Computer Science Series
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı
dc.rightsinfo:eu-repo/semantics/openAccess
dc.snmzKA_WoS_20260121
dc.subjectInverse problem
dc.subjectFractional derivative
dc.subjectPseudo-parabolic equation
dc.subjectTikhonov regularization
dc.subjectStability analysis
dc.subjectNonlinear optimization
dc.titleAn Inverse Problem of Reconstructing the Unknown Coefficient in a Third Order Time Fractional Pseudoparabolic Equation
dc.typeArticle

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