mmnsa

Mathematical Modelling and Numerical Simulation with Applications

2791-8564

Mehmet YAVUZ

10.53391/mmnsa.1503311

Mathematical Optimisation Applied Mathematics (Other)

Matematikte Optimizasyon Uygulamalı Matematik (Diğer)

Fractional-order model of the post-disaster period: study on the earthquakes in Türkiye

https://orcid.org/0000-0002-8546-612X

Daşbaşı

Teslima

Kayseri University, Bünyan Vocational School, Department of Property Protection and Security, 38600 Kayseri

https://orcid.org/0000-0001-8201-7495

Daşbaşı

Bahatdin

Kayseri University, Faculty of Engineering, Architecture and Design, Department of Engineering Basic Sciences, 38280 Kayseri

03 31 2025

5 1 117 142 06 24 2024 03 12 2025

2021

Mathematical Modelling and Numerical Simulation with Applications

In this study, the mathematical model that examined the relationships between the variables of the population that continued to live in the disaster area, the population that migrated to another region, the number of newly built independent sections in the disaster area the post-disaster, and the socio-economic development index (SEDI) of the disaster area is expressed through fractional-order differential equations (FODEs) and qualitative analysis of the model is carried out. Furthermore, the relationship between migrated and non-migrated populations is presented in the model with four different functional responses. In real-world applications of the model, some earthquakes in Türkiye, which are similar to each other in many ways, are taken into account. Therefore, data after the Gölcük earthquake in 1999 are used, and parameters, derivative order, and functional response are determined by considering the minimum root mean squared error (RMSE). Then, the performance of the proposed model with these values is shown in the Elbistan earthquake in 2023. Finally, the 5-year and 10-year estimates of the non-migratory population, the migrated population, the number of newly built independent sections, and the SEDI index values are presented for Elbistan.

Fractional-order differential equation functional response earthquakes; socio-economic development index root mean squared error

TUBITAK 123F220

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