THERMAL SCIENCE

International Scientific Journal

Nichaphat Patanarapeelert

,

Asma Asma

,

Arshad Ali

,

Kamal Shah

,

Thabet Abdeljawad

,

Thanin Sitthiwirattham

STUDY OF A COUPLED SYSTEM WITH ANTI-PERIODIC BOUNDARY CONDITIONS UNDER PIECEWISE CAPUTO-FABRIZIO DERIVATIVE

ABSTRACT
A coupled system under Caputo-Fabrizio fractional order derivative (CFFOD) with antiperiodic boundary condition is considered. We use piecewise version of CFFOD. Sufficient conditions for the existence and uniqueness of solution by ap­plying the Banach, Krasnoselskii's fixed point theorems. Also some appropriate results for Hyers-Ulam (H-U) stability analysis is established. Proper example is given to verify the results.
KEYWORDS
piecewise CFFOD, stability results, fixed point technique
PAPER SUBMITTED: 2022-03-15
PAPER REVISED: 2022-04-14
PAPER ACCEPTED: 2022-04-24
PUBLISHED ONLINE: 2023-04-08
DOI REFERENCE: https://doi.org/10.2298/TSCI23S1287P
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2023, VOLUME 27, ISSUE Special issue 1, PAGES [287 - 300]
REFERENCES
  1. Machado, J. T., et al., Recent History of Fractional Calculas, Comun. Non-l. Sci. Num. Simul., 16 (2011), 3, pp. 1140-1153
  2. Loverro, A., Fractional Calculus: History, Definitions and Applications for the Engineer, Rapport Technique, Univeristy of Notre Dame: Department of Aerospace and Mechanical Engineering, 2004, pp. 1-28
  3. Kilbas, A. A., et al., Theory and Applications of Fractional Differential Equations, Elesvier, North-Holland Mathematics studies, Amesterdam, The Netherlands, 2006
  4. Hilfer, R., Threefold Introduction Fractional Derivatives, in: Anomalous Transport: Foundations and Applications, Willy, New York, USA, 2008
  5. Miller, K. S., Ross, B., An Introduction the Fractional Calculas and Fractional Differential Equations, John Wiley and Sons, New York, USA, 1993
  6. Agarwal, R., et al., A Survey on Similar Differential Equations and Inclusions Involving Riemann-Liouville Fractional Derivative, Journal Adv. Diff. Equ., 10 (2009), Mar., pp. 857-868
  7. Lakshmikantham, V., Vatsala, A. S., Basic Theory of Fractional Differential Equations, Non-Linear Analysis: Theory, Methods and Applications, 69 (2008), 8, pp. 2677-2682
  8. Alshabanat, A., et al., Generalization of Caputo-Fabrizio Fractional Derivative and Applications to Electrical Circuits, Frontiers in Physics, 64 (2020), 14
  9. Dokuyucu, M. A., et al., Cancer Treatment Model with the Caputo-Fabrizio Fractional Derivative, European Physical Journal Plus, 133 (2018), 3, pp. 1-6
  10. Caputo, M., Fabrizio, M., On the Notion of Fractional Derivative and Applications to the Hysteresis Phenomena, Meccanica, 52 (2017), 13, pp.3043-3052
  11. Qureshi, S., et al., New Numerical Aspects of Caputo-Fabrizio Fractional Derivative Operator, Mathematics, 7 (2019), 4, 374
  12. Verma, P., Kumar, M., Analysis of a Novel Coronavirus (2019-nCOV) System with Variable Caputo-Fabrizio Fractional Order, Chaos, Solitons and Fractals, 142 (2021), 110451
  13. Algahtani, O. J. J., Comparing the Atangana-Baleanu and Caputo-Fabrizio Derivative with Fractional Order: Allen Cahn model, Chaos, Solitons and Fractals, 89 (2016), Aug., pp. 552-559
  14. Abdeljawad, T., Fractional Operators with Exponential Kernels and a Lyapunov Type Inequality, Adv. Diff. Equn., 2017 (2017), 313, pp. 1-11
  15. Liu, K., et al., Hyers-Ulam Stability and Existence of Solutions for Differential Equations with Caputo-Fabrizio Fractional Derivative, Mathematics, 7 (2019), 4, 333
  16. Eiman, S. K., et al., Study on Krasnoselskii's Fixed Point Theorem for Caputo-Fabrizio Fractional Differential Equations, Advances in Difference Equations, 2020 (2020), 1, pp. 1-9
  17. Atangana, A., Baleanu, D., New Fractional Derivatives with Non-Local and Non-Singular Kernel: Theory and Application Heat Transfer Model, Thermal Science, 20 (2016), 2. pp. 763-769
  18. Atangana, A., Baleanu, D., Caputo-Fabrizio Derivative Applied to Groundwater Flow within Confined Aquifer, Journal of Engineering Mechanics, 143 (2017), 5, ID4016005
  19. Atangana, A., Koca, I., Chaos in a Simple Non-Linear System with Atangana-Baleanu Derivatives with Fractional Order, Chaos, Solitons and Fractals, 89 (2016), Aug., pp. 447-454
  20. Liu, K., et al., A Fixed-Point Approach to the Hyers-Ulam Stability of Caputo-Fabrizio Fractional Differential Equations, Mathematics, 8 (2020), 4, 647
  21. Atangana, A., et al., Decolonisation of Fractional Calculus Rules: Breaking Commutativity and Associativity to Capture More Natural Phenomena, The European Physical Journal Plus, 133 (2018), 4, pp. 1-22
  22. Atangana, A., On the New Fractional Derivative and Application Non-Linear Fisher's Reaction-Diffusion Equation, Applied Mathematics and Computation, 273 (2016), Jan., pp. 948-956
  23. Khan, H., et al., Existence and Data Dependence Theorems for Solutions of an ABC-Fractional Order Impulsive System, Chaos, Solitons and Fractals, 131 (2020), 109477
  24. Baleanu, D., et al., On Existence Results for Solutions of a Coupled System of Hybrid Boundary Value Problems with Hybrid Conditions, Advances in Difference Equations, 2015 (2015), 1, pp. 1-14
  25. Petra, I., Magin, R. L., Simulation of Drug Uptake in a Two Compartmental Fractional Model for a Biological System, Communications in Non-Linear Science and Numerical Simulation, 16 (2011), 12, pp. 4588-4595
  26. Aqlan, M. H., et al., Existence Theory for Sequential Fractional Differential Equations with Anti-Periodic Type Boundary Conditions, Open Mathematics, 14 (2016), 1, pp. 723-735
  27. Atangana, A., Araz, S. I., New Concept in Calculus: Piecewise Differential and Integral Operators, Chaos, Solitons and Fractals, 145 (2021), 110638
  28. Shah, K., et al., Mathematical Analysis of the Cauchy Type Dynamical System under Piecewise Equations with Caputo Fractional Derivative, Chaos, Solitons and Fractals, 161 (2022), 112356
PDF VERSION [DOWNLOAD]
Study of a coupled system with anti-periodic boundary conditions under piecewise Caputo-Fabrizio derivative

© 2024 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence