Nonlinear equations with global differential and integral operators: Existence, uniqueness with application to epidemiology

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dc.authoridIGRET ARAZ, SEDA/0000-0002-7698-0709
dc.contributor.authorAtangana, Abdon
dc.contributor.authorAraz, Seda Igret
dc.date.accessioned2024-12-24T19:27:36Z
dc.date.available2024-12-24T19:27:36Z
dc.date.issued2021
dc.departmentSiirt Üniversitesi
dc.description.abstractVery recently, the concept of instantaneous change was extended with the aim to accommodate prediction of more complex real world problems that could not be predicted or depicted by the existing rate of change. The extension gave birth to a more general differential operator that to be a derivative associate to the well-known Riemann-Stieltjes integral. In addition to this, using specific functions, one is able to recover all existing local differential operators defined as rate of change. This extended concept is still at its genesis and more works need to be done to establish a Riemann-Stieltjes calculus. In this paper, we aim to present a detailed analysis of an important class of differential equations called stochastic equations with the new classes of differential operators with the global derivative with integer and non-integer orders. We considered many classes as nonlinear Cauchy problems, then we presented existence and the uniqueness of their solutions using the linear growth and the Lipchitz conditions. We derived numerical solutions for each class and presented the error analysis. To show the applicability of these operators, we considered three epidemiological problems, including the zombie virus spread model, the zika virus spread model and Ebola model. We solved each model using the suggested numerical scheme and presented the numerical solutions for different values of fractional order and the global function g(t). Our results showed that, more complex real world problems could be depicted using these classes of differential equations.
dc.identifier.doi10.1016/j.rinp.2020.103593
dc.identifier.issn2211-3797
dc.identifier.scopus2-s2.0-85098515118
dc.identifier.scopusqualityQ1
dc.identifier.urihttps://doi.org/10.1016/j.rinp.2020.103593
dc.identifier.urihttps://hdl.handle.net/20.500.12604/6720
dc.identifier.volume20
dc.identifier.wosWOS:000614830200010
dc.identifier.wosqualityQ2
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.language.isoen
dc.publisherElsevier
dc.relation.ispartofResults in Physics
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı
dc.rightsinfo:eu-repo/semantics/openAccess
dc.snmzKA_20241222
dc.subjectGlobal rate of change
dc.subjectGlobal derivative
dc.subjectFractional kernels
dc.subjectZombie virus
dc.subjectZika virus
dc.subjectEbola virus
dc.titleNonlinear equations with global differential and integral operators: Existence, uniqueness with application to epidemiology
dc.typeArticle

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