Uyumlu Flett teoremi ve Sahoo ve Riedel teoremi

Öz

Karmaşık olayları modellemede kesirli analiz büyük ilgi çektiğinden, kesirli türevlerin özelliklerini araştırmak çok önemlidir. Bu çalışmada, uyumlu türev için ortalama değer teoreminin bir türü olan Flett teoremi ile Sahoo ve Riedel teoremlerini ilk kez vereceğiz.

Anahtar Kelimeler

• uyumlu türev
• Flett teoremi
• Sahoo ve Riedel teoremi

Conformable Flett’s theorem and Sahoo and Riedel theorem

Öz

Since fractional analysis has attracted considerable interest by virtue of their ability to model complex phenomena, it is crucial to investigate properties of fractional derivatives. In this research, accordingly, we first give the extension of Flett's theorem and Sahoo and Riedel theorem to conformable derivative as a variety of conformable mean value theorem.

Anahtar Kelimeler

• Conformable derivative
• Flett’s theorem
• Sahoo and Riedel theorem

Kaynakça

1. Uçar, E., Özdemir, N., A fractional model of cancer-immune system with Caputo and Caputo–Fabrizio derivatives, The European Physical Journal Plus 136(1), 1-17, (2021).
2. Özdemir, N., Uçar, E., Investigating of an immune system-cancer mathematical model with Mittag-Leffler kernel, AIMS Mathematics, 5(2), 1519-1531, (2020).
3. Özköse, F., Yavuz, M., Şenel, M. T., Habbireeh, R., Fractional order modelling of omicron SARS-CoV-2 variant containing heart attack effect using real data from the United Kingdom, Chaos Solitons & Fractals, 157, 111954, (2022).
4. Hammouch, Z., Yavuz, M., Özdemir, N., Numerical solutions and synchronization of a variable-order fractional chaotic system, Mathematical Modelling and Numerical Simulation with Applications, 1(1), 11-23, (2021).
5. Evirgen, F.,, Conformable Fractional Gradient Based Dynamic System for Constrained Optimization Problem, Acta Physica Polonica A, 132, 1066-1069, (2017).
6. Özköse, F., Şenel, M. T., Habbireeh, R., Fractional-order mathematical modelling of cancer, cells-cancer stem cells-immune system interaction with chemotherapy, Mathematical Modelling and Numerical Simulation with Applications, 1(2), 67-83, (2021).
7. Kaya, Y., Complex Rolle and Mean Value Theorems, MsC Thesis, Balıkesir University, (2015).
8. Uçar, S., Özgür, N. Y., Eroğlu, B. B. I., Complex Conformable Derivative, Arabian Journal of Geosciences, 12, 201, (2019).

9. Hamou, A. A., Rasul, R. R. Q., Hammouch, Z., Özdemir, N., Analysis and dynamics of a mathematical model to predict unreported cases of COVID-19 epidemic in Morocco, Computational and Applied Mathematics, 41(6), 1-33, (2022).
10. Hama, M. F., Rasul, R. R. Q., Hammouch, Z., K. A. H., Rasul, Analysis of a stochastic SEIS epidemic model with the standard Brownian motion and Levy jump, Results in Physics, 37, 105477, (2022).
11. Alkahtani, B. S. T., Koca, İ. Fractional stochastic sır model, Results in Physics, 24, 104124, (2021).
12. Durur, H., Yokuş, A., Yavuz, M., Behavior Analysis and Asymptotic Stability of the Traveling Wave Solution of the Kaup-Kupershmidt Equation for Conformable Derivative Fractional Calculus: New Applications in Understanding Nonlinear Phenomena 3, 162 (2022).
13. Yel, G., Kayhan, M., Ciancio, A., A new analytical approach to the (1+1)-dimensional conformable Fisher equation. Mathematical Modelling and Numerical Simulation with Applications, 2(4), 211-220, (2022).
14. Naim, M., Sabbar, Y., Zeb, A., Stability characterization of a fractional-order viral system with the non-cytolytic immune assumption, Mathematical Modelling and Numerical Simulation with Applications, 2(3), 164-176, (2022).
15. Yavuz, M. Özdemir, N., On the Solutions of Fractional Cauchy Problem Featuring Conformable Derivative, ITM Web of Conferences, 22, (2018).
16. Podlubny, I., Fractional Differential Equations: An Introduction to Fractional Derivatives to Methods of their Solution and Some of their Applications, Academic Press, (1998).
17. Yavuz, M., Novel solution methods for initial boundary value problems of fractional order with conformable differentiation, An International Journal of Optimization and Control Theories & Applications (IJOCTA), 8(1), 1-7, (2018).
18. Atangana, A., Baleanu, D., New fractional derivatives with non-local and non-singular kernel theory and applications to heat transfer model, Thermal Science, 20, 763-769, (2016).
19. Joshi, H., Jha, B. K., Chaos of calcium diffusion in Parkinson’s infectious disease model and treatment mechanism via Hilfer fractional derivative, Mathematical Modelling and Numerical Simulation with Applications, 1(2), 84-94, (2021).
20. Uçar, S. Özdemir, N., Koca. İ., Altun, E. Novel analysis of the fractional glucose–insulin regulatory system with non-singular kernel derivative, The European Physical Journal Plus, 135(5), (2020).
21. Koca, İ., Numerical analysis of coupled fractional differential equations with Atangana- Baleanu fractional derivative, Discrete & Continuous Dynamical Systems-S, 12(3), 475-486, (2019).
22. Evirgen, F., Transmission of Nipah virus dynamics under Caputo fractional derivative, Journal of Computational and Applied Mathematics, 418, (2023).
23. Khalil, R., Al Horani, M., Yousef, A., Sababheh, M., A new definition of fractional derivative, Journal of Computational and Applied Mathematics, 264 65-70, (2014).
24. Flett, T. M., A mean value theorem, Mathematical Gazette, 42, 38–39, (1958). Sahoo, P. K., Riedel, T., Mean Value Theorems and Functional Equations, World Scientific, (1998).