Ulam's stability of conformable neutral fractional differential equations
DOI:
https://doi.org/10.5269/bspm.51442Resumen
This article is concerned with the existence and uniqueness of solutions of a nonlinear neutral conformable fractional differential system with infinite delay, involving conformable fractional derivative. Additionally, we study the Ulam--Hyres stability, Ulam--Hyres--Mittag--Leffler stability, Ulam--Hyres--Mittag--Leffler--Rassias stability for the solutions of considered system using Picard operator. For application of the theory, we add an example at the end.
Referencias
1. Abdeljawad, T., On conformable fractional calculus, J. Comput. Appl. Math., 279, 57-66 (2015) https://doi.org/10.1016/j.cam.2014.10.016
2. Ahmad, B., Ntouyas, S. K., Alsaedi, A., Alnahdi, M., Existence theory for fractional-order neutral boundary value problems, Frac. Differ. Calc., 8, 111-126 (2018) https://doi.org/10.7153/fdc-2018-08-07
3. Ahmad, A., Zada, A., Wang, X., Existence, uniqueness and stability of implicit switched coupled fractional differential equations of ψ-Hilfer type, Int. J. Nonlin. Sci. Num., 21 , no. 3-4, 327-337 (2020). https://doi.org/10.1515/ijnsns-2018-0371
4. Ahmad, M., Zada, A., Alzabut, J., Stability analysis of a nonlinear coupled implicit switched singular fractional differential system with p−Laplacian, Adv. Differ. Equ., 2019:436, 1-22 (2019), https://doi.org/10.1186/s13662-019-2367-y
5. Ahmad, M., Zada, A., Alzabut, J., Hyers-Ulam stability of a coupled system of fractional differential equations of Hilfer-Hadamard type, Demonstr. Math., 52, 283-295 (2019) https://doi.org/10.1515/dema-2019-0024
6. Baleanu, D., Machado, J., Luo, A., Fractional Dynamics and Control, Springer., 2012 https://doi.org/10.1007/978-1-4614-0457-6
7. Balachandran, K., Park, J. Y., Controllability of fractional integrodifferential systems in Banach spaces, Nonlinear Analysis: Hybrid Systems, 3, 363-367 (2009) https://doi.org/10.1016/j.nahs.2009.01.014
8. Bayour, B., Torres, D. F. M., Existence of solution to a local fractional nonlinear differential equation, J. Comput. Appl. Math., 312, 127-133 (2017) https://doi.org/10.1016/j.cam.2016.01.014
9. Chen, W. H., Zheng, W. X., Delay-dependent robust stabilization for uncertain neutral systems with distributed delays, Automatica, 43, 95-104 (2007) https://doi.org/10.1016/j.automatica.2006.07.019
10. Diethelm, K., The Analysis of Fractional Differential Equations, Lecture Notes in Mathematics., 2010 https://doi.org/10.1007/978-3-642-14574-2
11. Dong, X., Bai, Z., Zhang, W., Positive solutions for nonlinear eigenvalue problems with conformable fractional differential derivatives, J. Shandong Univ. Sci. Technol. Nat. Sci., 35, 85-90 (2016)
12. Eslami, M., Exact traveling wave solutions to the fractional coupled nonlinear Schrodinger equations, Appl. Math. Comput., 285, 141-148 (2016) https://doi.org/10.1016/j.amc.2016.03.032
13. Ekici, M., Mirzazadeh, M., Optical soliton perturbation with fractional-temporal evolution by first integral method with conformable fractional derivatives, Optik, 127, 10659-19669 (2016) https://doi.org/10.1016/j.ijleo.2016.08.076
14. Granas, A., Dugundji, J., Fixed point theory, Springer-Verlag, New York, 2003 https://doi.org/10.1007/978-0-387-21593-8
15. Khalil, R., Sababheh, M., A new definition of fractional derivative, J. Comput. Appl. Math., 264, 65-70 (2014) https://doi.org/10.1016/j.cam.2014.01.002
16. Lakshmikantham, V., Leela, S., Devi, J. V., Theory of Fractional Dynamic Systems, Cambridge Scientific Publishers., 2009.
17. Miller, K. S., Ross, B., An Introduction to the Fractional Calculus and Differential Equations, John Wiley., 1993
18. Podlubny, I., Fractional Differential Equations, Academic Press., 1999
19. Sun, H., Zhang, Y., Baleanu, D., Chen, W., Chen, Y., A new collection of real world applications of fractional calculus in science and engineering, Commun Nonlinear Sci Numer Simulat., 64, 213-231 (2018) https://doi.org/10.1016/j.cnsns.2018.04.019
20. Riaz, U., Zada, A., Ali, Z., Ahmad, M., Xu, J., Fu, Z., Analysis of Nonlinear Coupled Systems of Impulsive Fractional Differential Equations with Hadamard Derivatives, Math. Probl. Eng., 2019, 1-20 (2019) https://doi.org/10.1155/2019/5093572
21. Rizwan, R., Zada, A., Wang, X., Stability analysis of non linear implicit fractional Langevin equation with non-instantaneous impulses, Adv. Differ. Equ., 2019 85 (2019) https://doi.org/10.1186/s13662-019-1955-1
22. Wang, J. R., Zada, A., Waheed, H., Stability analysis of a coupled system of nonlinear implicit fractional anti-periodic boundary value problem, Math. Meth. App. Sci., 42, 6706-6732 (2019) https://doi.org/10.1002/mma.5773
23. Zada, A., Ali, S., Li, T., Analysis of a new class of impulsive implicit sequential fractional differential equations, Int. J. Nonlin. Sci. Num., (2020). DOI: 10.1515/ijnsns-2019-0030 https://doi.org/10.1515/ijnsns-2019-0030
24. Zada, A., Alzabut, J., Waheed, H., Popa, I. L., Ulam-Hyers stability of impulsive integrodifferential equations with Riemann-Liouville boundary conditions, Adv. Differ. Equ., 2020, 64 (2020) https://doi.org/10.1186/s13662-020-2534-1
25. Zhou, Y., Basic Theory of Fractional Differential Equations, World Scientific., 2014 https://doi.org/10.1142/9069
2. Ahmad, B., Ntouyas, S. K., Alsaedi, A., Alnahdi, M., Existence theory for fractional-order neutral boundary value problems, Frac. Differ. Calc., 8, 111-126 (2018) https://doi.org/10.7153/fdc-2018-08-07
3. Ahmad, A., Zada, A., Wang, X., Existence, uniqueness and stability of implicit switched coupled fractional differential equations of ψ-Hilfer type, Int. J. Nonlin. Sci. Num., 21 , no. 3-4, 327-337 (2020). https://doi.org/10.1515/ijnsns-2018-0371
4. Ahmad, M., Zada, A., Alzabut, J., Stability analysis of a nonlinear coupled implicit switched singular fractional differential system with p−Laplacian, Adv. Differ. Equ., 2019:436, 1-22 (2019), https://doi.org/10.1186/s13662-019-2367-y
5. Ahmad, M., Zada, A., Alzabut, J., Hyers-Ulam stability of a coupled system of fractional differential equations of Hilfer-Hadamard type, Demonstr. Math., 52, 283-295 (2019) https://doi.org/10.1515/dema-2019-0024
6. Baleanu, D., Machado, J., Luo, A., Fractional Dynamics and Control, Springer., 2012 https://doi.org/10.1007/978-1-4614-0457-6
7. Balachandran, K., Park, J. Y., Controllability of fractional integrodifferential systems in Banach spaces, Nonlinear Analysis: Hybrid Systems, 3, 363-367 (2009) https://doi.org/10.1016/j.nahs.2009.01.014
8. Bayour, B., Torres, D. F. M., Existence of solution to a local fractional nonlinear differential equation, J. Comput. Appl. Math., 312, 127-133 (2017) https://doi.org/10.1016/j.cam.2016.01.014
9. Chen, W. H., Zheng, W. X., Delay-dependent robust stabilization for uncertain neutral systems with distributed delays, Automatica, 43, 95-104 (2007) https://doi.org/10.1016/j.automatica.2006.07.019
10. Diethelm, K., The Analysis of Fractional Differential Equations, Lecture Notes in Mathematics., 2010 https://doi.org/10.1007/978-3-642-14574-2
11. Dong, X., Bai, Z., Zhang, W., Positive solutions for nonlinear eigenvalue problems with conformable fractional differential derivatives, J. Shandong Univ. Sci. Technol. Nat. Sci., 35, 85-90 (2016)
12. Eslami, M., Exact traveling wave solutions to the fractional coupled nonlinear Schrodinger equations, Appl. Math. Comput., 285, 141-148 (2016) https://doi.org/10.1016/j.amc.2016.03.032
13. Ekici, M., Mirzazadeh, M., Optical soliton perturbation with fractional-temporal evolution by first integral method with conformable fractional derivatives, Optik, 127, 10659-19669 (2016) https://doi.org/10.1016/j.ijleo.2016.08.076
14. Granas, A., Dugundji, J., Fixed point theory, Springer-Verlag, New York, 2003 https://doi.org/10.1007/978-0-387-21593-8
15. Khalil, R., Sababheh, M., A new definition of fractional derivative, J. Comput. Appl. Math., 264, 65-70 (2014) https://doi.org/10.1016/j.cam.2014.01.002
16. Lakshmikantham, V., Leela, S., Devi, J. V., Theory of Fractional Dynamic Systems, Cambridge Scientific Publishers., 2009.
17. Miller, K. S., Ross, B., An Introduction to the Fractional Calculus and Differential Equations, John Wiley., 1993
18. Podlubny, I., Fractional Differential Equations, Academic Press., 1999
19. Sun, H., Zhang, Y., Baleanu, D., Chen, W., Chen, Y., A new collection of real world applications of fractional calculus in science and engineering, Commun Nonlinear Sci Numer Simulat., 64, 213-231 (2018) https://doi.org/10.1016/j.cnsns.2018.04.019
20. Riaz, U., Zada, A., Ali, Z., Ahmad, M., Xu, J., Fu, Z., Analysis of Nonlinear Coupled Systems of Impulsive Fractional Differential Equations with Hadamard Derivatives, Math. Probl. Eng., 2019, 1-20 (2019) https://doi.org/10.1155/2019/5093572
21. Rizwan, R., Zada, A., Wang, X., Stability analysis of non linear implicit fractional Langevin equation with non-instantaneous impulses, Adv. Differ. Equ., 2019 85 (2019) https://doi.org/10.1186/s13662-019-1955-1
22. Wang, J. R., Zada, A., Waheed, H., Stability analysis of a coupled system of nonlinear implicit fractional anti-periodic boundary value problem, Math. Meth. App. Sci., 42, 6706-6732 (2019) https://doi.org/10.1002/mma.5773
23. Zada, A., Ali, S., Li, T., Analysis of a new class of impulsive implicit sequential fractional differential equations, Int. J. Nonlin. Sci. Num., (2020). DOI: 10.1515/ijnsns-2019-0030 https://doi.org/10.1515/ijnsns-2019-0030
24. Zada, A., Alzabut, J., Waheed, H., Popa, I. L., Ulam-Hyers stability of impulsive integrodifferential equations with Riemann-Liouville boundary conditions, Adv. Differ. Equ., 2020, 64 (2020) https://doi.org/10.1186/s13662-020-2534-1
25. Zhou, Y., Basic Theory of Fractional Differential Equations, World Scientific., 2014 https://doi.org/10.1142/9069
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2022-12-23
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