Have a personal or library account? Click to login

Lakshmikantham Monotone Iterative Principle for Hybrid Atangana-Baleanu-Caputo Fractional Differential Equations

Open Access
|May 2023

References

  1. S. Abbas, M. Benchohra, J.R. Graef, J. Henderson, Implicit Fractional Differential and Integral Equations: Existence and Stability, De Gruyter, Berlin, 2018.
  2. S. Abbas, M. Benchohra, G. M. N’Guérékata, Topics in Fractional Differential Equations, Springer, New York, 2012.
  3. S. Abbas, M. Benchohra, G. M. N’Guérékata, Advanced Fractional Differential and Integral Equations, Nova Science Publishers, New York, 2015.
  4. M. S. Abdo, T. Abdeljawad, K. D. Kishor, M. A. Alqudah, M. A. Saeed, M. B. Jeelani, On nonlinear pantograph fractional differential equations with Atangana-Baleanu-Caputo derivative, Adv. Difference Equ. (2021), Paper No. 65, 17 pp
  5. R. S. Adiguzel, U. Aksoy, E. Karapinar, I.M. Erhan, On the solution of a boundary value problem associated with a fractional differential equation, Math. Methods Appl. Sci., https://doi.org/10.1002/mma.6652
  6. R. S. Adiguzel, U. Aksoy, E. Karapinar, I.M. Erhan, Uniqueness of solution for higher-order nonlinear fractional differential equations with multi-point and integral boundary conditions, RACSAM (2021), 115-155, https://doi.org/10.1007/s13398-021-01095-3
  7. R. S. Adiguzel, U. Aksoy, E. Karapinar, I.M. Erhan, On the solutions of fractional differential equations via Geraghty type hybrid contractions, Appl. Comput. Math. 20 (2021), 313-333.
  8. H. Akhadkulov, F. Alsharari, T. Y. Ying, Applications of Krasnoselskii-Dhage type fixed-point Theorems to fractional hybrid differential equations, Tamkang J. Math. 52 (2) (2021), 281-292.
  9. B. Alqahtani, H. Aydi, E. Karapinar, V. Rakocevic, A solution for Volterra fractional integral equations by hybrid contractions, Mathematics 7 (2019), 694, https://doi.org/10.3390/math7080694
  10. A. Atangana, On the new fractional derivative and application to nonlinear Fisher’s reaction-diffusion equation, Appl. Math. Comput. 273 (2016), 948-956.
  11. A. Atangana, B. S. Alkahtani, Analysis of the Keller-Segel model with a fractional derivative without singular kernel, Entropy 17 (2015), 4439-4453.
  12. A. Atangana, D. Baleanu, New fractional derivatives with nonlocal and non-singular kernel: Theory and application to heat transfer model, Therm. Sci. 20 (2016), 763-769.
  13. A. Atangana, D. Baleanu, Caputo-Fabrizio derivative applied to groundwater flow with in confined aquifer, J. Eng. Mech. (2016), 5 pages.
  14. M. Caputo, M. Fabrizio, A new definition of fractional derivative without singular kernel, Prog. Fract. Differ. Appl. 1 (2) (2015), 73-85.
  15. B.C. Dhage, Some variants of two basic hybrid fixed point theorems of Krasnoselskii and Dhage with applications, Nonlinear Stud. 25 (2018), 559-573.
  16. B. C. Dhage, Hybrid fixed point theory in partially ordered normed linear spaces and applications to fractional integral equations, Differ. Equ. Appl. 5 (2013), 155-184.
  17. B. C. Dhage, Global attractivity results for comparable solutions of nonlinear hybrid fractional integral equations, Differ. Equ. Appl. 6 (2014), 165-186.
  18. B. C. Dhage, Partially condensing mappings in ordered normed linear spaces and applications to functional integral equations, Tamkang J. Math. 45 (4) (2014), 397-426.
  19. B. C. Dhage, Nonlinear D-set-contraction mappings in partially ordered normed linear spaces and applications to functional hybrid integral equations, Malaya J. Mat. 3 (1) (2015), 62-85.
  20. B. C. Dhage, N. S. Jadhav, Basic results in the theory of hybrid differential equations with linear perturbations of second type, Tamkang J. Math. 44 (2013), 171-186.
  21. B. D. Karande, S. N. Kondekar, Existence of solution to a quadratic functional integrodifferential fractional equation, Commun. Math. Appl. 11 (4) (2020), 635-650.
  22. E. Karapinar, H. D. Binh, N. H. Luc, N. H. Can, On continuity of the fractional derivative of the time-fractional semilinear pseudo-parabolic systems, Adv. Differ. Equ. 2021 (2021), 70, https://doi.org/10.1186/s13662-021-03232-z
  23. E. Karapinar, A. Fulga, M. Rashid, L. Shahid, H. Aydi, Large contractions on quasi-metric spaces with an application to nonlinear fractional differential-equations, Mathematics 7 (2019), 444, https://doi.org/10.3390/math7050444
  24. K. D. Kucche, S. T. Sutar, Analysis of nonlinear fractional differential equations involving Atangana-Baleanu-Caputo derivative, Chaos Solitons Fractals 143 (2021), 9 pp.
  25. K. D. Kucche, S. T. Sutar, On nonlinear hybrid fractional differential equations with Atangana-Baleanu-Caputo derivative, Chaos Solitons Fractals 143 (2021), 11 pp.
  26. J. E. Lazreg, S. Abbas, M. Benchohra, E. Karapinar, Impulsive Caputo-Fabrizio fractional differential equations in b-metric spaces, Open Math. 19 (2021), 363-372, https://doi.org/10.1515/math-2021-0040
  27. H. Lu, S. Sun, D. Yang, H. Teng, Theory of fractional hybrid differential equations with linear perturbations of second type, Bound. Value Probl. 23 (2013) 1-16.
  28. Y. Zhou, Basic Theory of Fractional Differential Equations, World Scientific, Singapore, 2014.
DOI: https://doi.org/10.2478/awutm-2023-0007 | Journal eISSN: 1841-3307 | Journal ISSN: 1841-3293
Language: English
Page range: 79 - 91
Published on: May 3, 2023
Published by: West University of Timisoara
In partnership with: Paradigm Publishing Services
Publication frequency: Volume open

© 2023 Nadia Benkhettou, Abdelkrim Salim, Jamal Eddine Lazreg, Saïd Abbas, Mouffak Benchohra, published by West University of Timisoara
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.