An inverse problem of recovering the heat source coefficient in a fourth-order time-fractional pseudo-parabolic equation

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dc.authorid0000-0003-4442-7498
dc.authorid0000-0001-5247-2913
dc.authorid0000-0001-6725-5663
dc.contributor.authorHuntul, M. J.
dc.contributor.authorTekin, I.
dc.contributor.authorIqbal, Muhammad Kashif
dc.contributor.authorAbbas, Muhammad
dc.date.accessioned2026-01-24T12:31:07Z
dc.date.available2026-01-24T12:31:07Z
dc.date.issued2024
dc.departmentAlanya Alaaddin Keykubat Üniversitesi
dc.description.abstractIn this paper, we have considered the problem of recovering the time dependent source term for the fourth order time fractional pseudoparabolic equation theoretically and numerically, for the first time, by considering an additional measurement at the left boundary of the space interval. This is very challenging and interesting inverse problem with many important applications in various fields of physics and mechanics. The existence of unique solution to the problem has been discussed by means of the contraction principle and Banach Fixed-point theorem 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 illposed (very slight errors in the additional input may cause relatively significant errors in the output force), 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 forcing term. The proposed problem is discretized using the quintic B-spline (QnB-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 analytical and perturbed data are inverted and the numerical outcomes for two benchmark test examples are reported and discussed.
dc.identifier.doi10.1016/j.cam.2023.115712
dc.identifier.issn0377-0427
dc.identifier.issn1879-1778
dc.identifier.scopus2-s2.0-85178565218
dc.identifier.scopusqualityQ1
dc.identifier.urihttps://doi.org/10.1016/j.cam.2023.115712
dc.identifier.urihttps://hdl.handle.net/20.500.12868/5654
dc.identifier.volume442
dc.identifier.wosWOS:001131972500001
dc.identifier.wosqualityQ1
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.language.isoen
dc.publisherElsevier
dc.relation.ispartofJournal of Computational and Applied Mathematics
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı
dc.rightsinfo:eu-repo/semantics/closedAccess
dc.snmzKA_WoS_20260121
dc.subjectInverse problem
dc.subjectFractional derivative
dc.subjectPseudo-parabolic equation
dc.subjectStability analysis
dc.subjectTikhonov regularization
dc.subjectNonlinear optimization
dc.titleAn inverse problem of recovering the heat source coefficient in a fourth-order time-fractional pseudo-parabolic equation
dc.typeArticle

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