Article detail · 2021
Nonlinear equations with global differential and integral operators: Existence, uniqueness with application to epidemiology
- Year
- 2021
- Type
- article
Data source split
- YÖKSİS YÖKSİS article record
- YÖKSİS venue Results in Physics
- Catalog match (ISSN) Results in Physics
- OpenAlex OpenAlex enrichment (abstract, citations, topics)
Abstract
OpenAlex · English
Very 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 gt. Our results showed that, more complex real world problems could be depicted using these classes of differential equations.
Topics
Citations
OpenAlex cited_by_count. Not a WoS or Scopus citation count; those sources have no separate column here.
86 citations
OpenAlex cited_by_count (cache / database)
18 publications in the local catalog that cite this work (OpenAlex reference match; not the full global list).
- New concept in calculus: Piecewise differential and integral operators 2021
- Modeling and forecasting the spread of COVID-19 with stochastic and deterministic approaches: Africa and Europe 2021
- A novel Covid-19 model with fractional differential operators with singular and non-singular kernels: Analysis and numerical scheme based on Newton polynomial 2021
- A fractional order Zika virus model with Mittag Leffler kernel 2021
- Modeling third waves of Covid-19 spread with piecewise differential and integral operators: Turkey, Spain and Czechia 2021
- A mathematical model for the dynamics of SARS-CoV-2 virus using the Caputo-Fabrizio operator 2021
- Effects of the quarantine on the individuals’ risk of Covid-19 infection: Game theoretical approach 2021
- A numerical study of dengue internal transmission model with fractional piecewise derivative 2022
- Effects of the quarantine on the individuals' risk of Covid-19 infection: Game theoretical approach 2021
- Fractional stochastic sır model 2021