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

[1] S. Abbas, M. Benchohra, J.R. Graef, J. Henderson, Implicit Fractional Differential and Integral Equations: Existence and Stability, De Gruyter, Berlin, 2018.Search in Google Scholar

[2] S. Abbas, M. Benchohra, G. M. N’Guérékata, Topics in Fractional Differential Equations, Springer, New York, 2012.Search in Google Scholar

[3] S. Abbas, M. Benchohra, G. M. N’Guérékata, Advanced Fractional Differential and Integral Equations, Nova Science Publishers, New York, 2015.Search in Google Scholar

[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 ppSearch in Google Scholar

[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.6652Search in Google Scholar

[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/s13398-021-01095-3Search in Google Scholar

[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.Search in Google Scholar

[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.Search in Google Scholar

[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/math7080694Search in Google Scholar

[10] A. Atangana, On the new fractional derivative and application to nonlinear Fisher’s reaction-diffusion equation, Appl. Math. Comput. 273 (2016), 948-956.Search in Google Scholar

[11] A. Atangana, B. S. Alkahtani, Analysis of the Keller-Segel model with a fractional derivative without singular kernel, Entropy 17 (2015), 4439-4453.Search in Google Scholar

[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.Search in Google Scholar

[13] A. Atangana, D. Baleanu, Caputo-Fabrizio derivative applied to groundwater flow with in confined aquifer, J. Eng. Mech. (2016), 5 pages.Search in Google Scholar

[14] M. Caputo, M. Fabrizio, A new definition of fractional derivative without singular kernel, Prog. Fract. Differ. Appl. 1 (2) (2015), 73-85.Search in Google Scholar

[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.Search in Google Scholar

[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.Search in Google Scholar

[17] B. C. Dhage, Global attractivity results for comparable solutions of nonlinear hybrid fractional integral equations, Differ. Equ. Appl. 6 (2014), 165-186.Search in Google Scholar

[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.Search in Google Scholar

[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.Search in Google Scholar

[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.Search in Google Scholar

[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.Search in Google Scholar

[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-zSearch in Google Scholar

[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/math7050444Search in Google Scholar

[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.Search in Google Scholar

[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.Search in Google Scholar

[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-2021-0040Search in Google Scholar

[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.Search in Google Scholar

[28] Y. Zhou, Basic Theory of Fractional Differential Equations, World Scientific, Singapore, 2014. Search in Google Scholar