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Exact separable solutions of two-dimensional time-fractional nonlinear biological population model under the regularized Prabhakar and ψ-Hilfer fractional-order derivatives

dc.rights.licenseopenen_US
dc.contributor.authorPRAKASH, P.
hal.structure.identifierLaboratoire de l'intégration, du matériau au système [IMS]
dc.contributor.authorVICTOR, Stéphane
ORCID: 0000-0002-0575-0383
IDREF: 148688942
dc.contributor.authorRAJ, Pavithra
dc.date.accessioned2025-09-08T08:10:33Z
dc.date.available2025-09-08T08:10:33Z
dc.date.issued2026-01
dc.identifier.issn1007-5704en_US
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/207574
dc.description.abstractEnThe main aim of this work is to investigate how to compute the exact separable solutions using the invariant subspace method for the fractional-order time derivative of two-dimensional nonlinear partial differential equations involving two space and one-time variables under two different fractional-order derivative definitions, namely the regularized Prabhakar and -Hilfer fractional-order derivatives. We also explicitly demonstrate the importance and usefulness of the method of the invariant subspace approach in computing the exact separable solutions for the two-dimensional fractional-order time derivative of the biological population model, which helps more accurately predict how populations will grow or shrink. More specifically, we show systematically how to compute the linear spaces for the above-mentioned model with the help of the invariant subspace approach. Furthermore, the computations of exact separable solutions are investigated for the linear and nonlinear biological population models under the above-mentioned two different time fractional-order derivatives with the help of the computed invariant linear spaces. Additionally, we notice that the computed solutions of the considered equations under the -Hilfer fractional derivative are valid under the -Riemann–Liouville, -Caputo, Hilfer, Katugampola, Caputo–Katugampola, Riemann–Liouville, and Caputo fractional derivatives because the -Hilfer fractional derivative is a generalization of those fractional derivatives. Also, note that the computed exact separable solutions to the underlying equation under two fractional-order derivatives are expressed in terms of trigonometric, exponential, and polynomial functions with two or three parameters of Mittag-Leffler functions. In addition, the obtained solutions under different fractional-order derivatives are compared with two-dimensional (2D) graphical representations. Finally, the exact separable solutions are presented for the initial and boundary value problems (IBVPs) of the discussed model under various fractional-order derivatives and their comparison.
dc.language.isoENen_US
dc.subject.enInvariant subspace method
dc.subject.enFractional-order biological population model
dc.subject.enExact solutions
dc.subject.enψ-Hilfer derivative
dc.subject.enRegularized Prabhakar fractional derivative
dc.subject.enInitial and boundary value problem
dc.title.enExact separable solutions of two-dimensional time-fractional nonlinear biological population model under the regularized Prabhakar and ψ-Hilfer fractional-order derivatives
dc.typeArticle de revueen_US
dc.identifier.doi10.1016/j.cnsns.2025.109145en_US
dc.subject.halSciences de l'ingénieur [physics]/Traitement du signal et de l'imageen_US
dc.subject.halInformatique [cs]/Traitement du signal et de l'imageen_US
bordeaux.journalCommunications in Nonlinear Science and Numerical Simulationen_US
bordeaux.page109145en_US
bordeaux.volume152en_US
bordeaux.hal.laboratoriesIMS : Laboratoire de l'Intégration du Matériau au Système - UMR 5218en_US
bordeaux.institutionUniversité de Bordeauxen_US
bordeaux.institutionBordeaux INPen_US
bordeaux.institutionCNRSen_US
bordeaux.peerReviewedouien_US
bordeaux.inpressnonen_US
bordeaux.import.sourcecrossref
hal.identifierhal-05244352
hal.version1
hal.date.transferred2025-09-08T08:10:37Z
hal.popularnonen_US
hal.audienceInternationaleen_US
hal.exporttrue
workflow.import.sourcecrossref
dc.rights.ccPas de Licence CCen_US
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Communications%20in%20Nonlinear%20Science%20and%20Numerical%20Simulation&rft.date=2026-01&rft.volume=152&rft.spage=109145&rft.epage=109145&rft.eissn=1007-5704&rft.issn=1007-5704&rft.au=PRAKASH,%20P.&VICTOR,%20St%C3%A9phane&RAJ,%20Pavithra&rft.genre=article


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