Theoretical and numerical analysis of a chaotic model with nonlocal and stochastic differential operators

Theoretical and numerical analysis of a chaotic model with nonlocal and stochastic differential operators

A set of nonlinear ordinary differential equations has been considered in this paper. The work tries to establish some theoretical and analytical insights when the usual time-deferential operator is replaced with the Caputo fractional derivative. Using the Caratheodory principle and other additional conditions, we established that the system has a unique system of solutions. A variety of well-known approaches were used to investigate the system. The stochastic version of this system was solved using a numerical approach based on Lagrange interpolation, and numerical simulation results were produced.

___

  • Ucar, E., Ozdemir, N., & Altun, E. (2023). Qualitative analysis and numerical simulations of new model describing cancer. Journal of Computational and Applied Mathematics, 422, 114899.
  • Zhang X-H, Algehyne E.A., Alshehri M.G., Bilal, M, Khan, M.A., & Muhammad, T. (2021). The parametric study of hybrid nanofluid flow with heat transition characteristics over a fluctuating spinning disk. Plos One. 16(8), e0254457.
  • Wang, B., Jahanshahi, H., Volos, C., Bekiros, S., Khan, M.A., Agarwal, P., & Aly, A.A. (2021). A new RBF neural network-based fault-tolerant active control for fractional time-delayed systems. Electronics. 10(12), 1501.
  • Abdullah, F.A., Islam, T., Gomez-Aguilar, J.F., & Akbar, A. (2023). Impressive and innovative soliton shapes for nonlinear Konno-Oono system relating to electromagnetic field. Optical and Quantum Electronics, 55, 69.
  • Attia, R.A.M., Tian, J., Lu, L., G ?omez-Aguilar, J.F., & Khater, M.M.A. (2022). Unstable novel and accurate soliton wave solutions of the nonlinear biological population model. Arab Journal of Basic and Applied Sciences. 29(1), 19-25.
  • Sheergojri A., Iqbal P., Agarwal P., & Ozdemir N. (2022). Uncertainty-based Gompertz growth model for tumor population and its numerical analysis. An International Journal of Optimization and Control: Theories & Applications (IJOCTA), 12, 137-150.
  • Sene, N. (2022). Theory and applications of new fractional-order chaotic system under Caputo operator. An International Journal of Optimization and Control: Theories & Applications, 12(1), 20- 38.
  • Evirgen, F. (2023). Transmission of Nipah virus dynamics under Caputo fractional derivative. Journal of Computational and Applied Mathematics, 418, 114654.
  • Evirgen, F., Ucar, E., Ucar, S., & Ozdemir, N. (2023). Modelling Influenza A disease dynamics under Caputo-Fabrizio fractional derivative with distinct contact rates. Mathematical Modelling and Numerical Simulation with Applications, 3(1), 58-72.
  • Dokuyucu, M.A., & Dutta H. (2020). A fractional order model for Ebola Virus with the new Ca- puto fractional derivative without singular kernel. Chaos, Solitons & Fractals, 134, 109717.
  • Atangana A., & Araz Igret S. (2021). New concept in calculus: Piecewise differential and integral operators. Chaos, Solitons & Fractals, 145, 110638.
  • Koca I. & Atangana A. (2022). Some Chaotic mathematical models with stochastic resetting. Fractals, 30(8), 2240212.
  • Miller, K.S., & Ross, B. (1993). An Introduction to the Fractional Calculus and Fractional Differential Equations, Wiley Hoboken, NJ, USA.
  • Podlubny, I. (1998). Fractional differential equations: an introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications. Vol. 198. Elsevier.
  • Cherif, A., Barley, K. (2011). Stochastic nonlinear dynamics of interpersonal and romantic relationships. Applied Mathematics and Computation, 217(13), 6273–6281.
  • Ozalp, N., & Koca, I. (2012). A fractional order nonlinear dynamical model of interpersonal relationships. Advances in Differential Equations, (2012)189.
  • Atangana, A., & Koca, I. (2023). Analytical and numerical investigation of the Hindmarsh- Rose model neuronal activity. Mathematical Biosciences and Engineering, 20(1), 1434-1459.
  • Robin, W.A. (2010). Solving differential equations using modified Picard iteration. International Journal of Mathematical Education in Science and Technology, 41(5).
  • Tonelli, L. (1928). Sulle equazioni funzionali del tipo di Volterra. Bull. of the Calcutta Math. Soc. 20, 31-48.
  • Peano, G. (1890). Demonstration de l’integrabilite des equations differentielles ordinaires. Mathematische Annalen. 37(2), 182–228.
  • Atangana, A. (2021). Mathematical model of survival of fractional calculus, critics and their im- pact: How singular is our world?. Advances in Difference Equations, (1), 1-59.
  • Toufik M, & Atangana A. (2017). New numerical approximation of fractional derivative with non-local and non-singular kernel: application to chaotic models. The European Physical Journal Plus, 132(10) 444.
An International Journal of Optimization and Control: Theories & Applications (IJOCTA)-Cover
  • ISSN: 2146-0957
  • Yayın Aralığı: Yılda 2 Sayı
  • Yayıncı: Prof. Dr. Ramazan YAMAN
Sayıdaki Diğer Makaleler

The effect of fractional order mathematical modelling for examination of academic achievement in schools with stochastic behaviors

Pelin Yaprakdal, ILKNUR KOCA, Kıvanç UZUN

Regional enlarged controllability of a fractional derivative of an output linear system

Rachıd LARHRISSI, Mustapha BENOUDİ

Adaptive MIMO fuzzy PID controller based on peak observer

Kemal UÇAK, Beyza Nur ARSLANTÜRK

A study on the approximate controllability results of fractional stochastic integro-differential inclusion systems via sectorial operators

Muthuvel Kothandapani, Kaliraj K.

Existence and stability analysis to the sequential coupled hybrid system of fractional differential equations with two different fractional derivatives

Prof. Dr. Jehad Alzabut, Mohamed HOUAS, Mahammad KHUDDUSH

Optimal C-type filter design for wireless power transfer system by using support vector machines

Haris ÇALGAN

Single-drone energy efficient coverage path planning with multiple charging stations for surveillance

Sule Itir Satoglu, Atalay ÇELİK, Enes USTAOMER

Theoretical and numerical analysis of a chaotic model with nonlocal and stochastic differential operators

ILKNUR KOCA, Abdon ATANGANA

Some stability results on non-linear singular differential systems with random impulsive moments

Michal FE KAN, Vinodkumar A, Harinie Sivakumar, Prof. Dr. Jehad Alzabut

Fractional fuzzy PI controller using particle swarm optimization to improve power factor by boost converter

Farhan AHMAD, Metin DEMİRTAŞ