On a class of fractional Langevin inclusion with multi-point boundary conditions
DOI:
https://doi.org/10.5269/bspm.62725Resumen
The aim of this paper deals with the existence results for a class of fractional langevin inclusion with multi-point boundary conditions. To prove the main results, we use the fixed theoreme for condensing multivalued maps, which is applicable to completely continuous operators. Our results extend and generalize several corespending results from the existing literature.
Referencias
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19. A. Salem and B. Alghamdi, Multi-strip and multi-point boundary conditions for fractional Langevin equation. Fractal and Fractional 4, 18, (2020). https://doi.org/10.3390/fractalfract4020018
20. A. Salem and B. Alghamdi, Multi-point and anti-periodic conditions for generalized Langevin equation with two fractional orders. Fractal and Fractional 3, 51,(2019) . https://doi.org/10.3390/fractalfract3040051
21. G. V. Smirnov, Introduction to the Theory of Differential Inclusions. Graduate Studies in Mathematics, American Mathematical Society vol 41, Providence, RI, USA, (2002). https://doi.org/10.1090/gsm/041
22. J. Yang, J. C. Ma, S. Zhao, and Y. Ge, Fractional multi-point boundary value problem of fractional differential equations. Mathematics in Practice and Theory 41, 188-194, (2011) .
23. Y. Zhou, Basic Theory of Fractional Differential Equations. Xiangtan University, China, 2014. https://doi.org/10.1142/9069
24. Z. Zhou, Y. Qiao, Solutions for a class of fractional Langevin equations with integral and anti-periodic boundary conditions. Boundary Value Problems 2018 (2018). https://doi.org/10.1186/s13661-018-1070-3
25. A. Lachouri, M. S. Abdo, A. Ardjouni, B. Abdalla and T. Abdeljawad. On a class of differential inclusions in the frame of generalized Hilfer fractional derivative. AIMS Mathematics, 7(3), 3477-3493, (2022). https://doi.org/10.3934/math.2022193
2. A. Cernea, On a multi point boundary value problem for a fractional order differential inclusion, Arab Journal of Mathematical Sciences 19, 73-83, (2013). https://doi.org/10.1016/j.ajmsc.2012.07.001
3. K. Deimling, Multivalued Differential Equations, Gruyter Series in Nonlinear Analysis and Applications vol. 1, Walter de Gruyter, Berlin, Germany, 1992.
4. H. Fazli and J. J. Nieto, Fractional Langevin equation with anti-periodic boundary conditions, Chaos, Solitons and Fractals 114, 332-337, (2018). https://doi.org/10.1016/j.chaos.2018.07.009
5. H. Fazli, H. G. Sun, and J. J. Nieto, Fractional Langevin equation involving two fractional orders: existence and uniqueness, Mathematics 8, 743, (2020). https://doi.org/10.3390/math8050743
6. A. Granas, J.Dugundji, Fixed Point Theory, Springer-Verlag, New York, (2005).
7. K. Hilal, K. Guida, L. Ibnelazyz, and M. Oukessou, Existence results for an impulsive fractional integro-differential equations with a non-compact semigroup, in Recent Advances in Intuitionistic Fuzzy Logic Systems, S. Melliani and O. Castillo, Eds., Studies in Fuzziness and Soft Computing pp. 191-211, (2019). https://doi.org/10.1007/978-3-030-02155-9_16
8. K. Hilal, L. Ibnelazyz, K. Guida, and S. Melliani, Existence of mild solutions for an impulsive fractional integrodifferential equations with non-local condition, in Recent Advances in Intuitionistic Fuzzy Logic Systems, S. Melliani and O. Castillo, Eds., Studies in Fuzziness and Soft Computing 251-271, (2019). https://doi.org/10.1007/978-3-030-02155-9_20
9. R. Hilfer, Applications of Fractional Calculs in Physics, World Scientific, Singapore, (2000). https://doi.org/10.1142/3779
10. S. Hu and N. S. Papageorgiou, Handbook of Multivalued Analysis, Mathematics and its Applications vol. 1, Kluwer Academic Publishers, Dordrecht, The Netherlands, (1997).
11. A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, NorthHolland Mathematics Studies, vol. 204, Elsevier, Amsterdam, (2006)
12. V. Lakshmikantham, Theory of fractional functional differential equations, Nonlinear Analysis: Theory, Methods and Applications 69, 3337-3343, (2008). https://doi.org/10.1016/j.na.2007.09.025
13. V. Lakshmikantham and A. S. Vatsala, Basic theory of fractional differential equations, Nonlinear Analysis: Theory, Methods and Applications 69, 2677-2682, (2008). https://doi.org/10.1016/j.na.2007.08.042
14. A. Lasota, Z. Opial An application of the Kakutani-Ky Fan theorem in the theory of ordinary differential equations, Bull Acad Polon Sci Ser Sci Math Astronom Phys. 13, 781-786, (1965).
15. C. Li, X. Luo, and Y. Zhou, Existence of positive solutions of the boundary value problem for nonlinear fractional differential equations, Computers and Mathematcs with Applications 59, 1363-1375, (2010). https://doi.org/10.1016/j.camwa.2009.06.029
16. K. S. Miller and B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations, Wiley, New York, NY, USA, (1993).
17. I. Podlubny, Fractional Differential Equations, Academic Press, New York, NY, USA, (1993).
18. M. Rehman, R. Khan, and N. Asif, Three point boundary value problems for nonlinear fractional differential equations, Acta Mathematica Scientia 31, 1337-1346, (2011). https://doi.org/10.1016/S0252-9602(11)60320-2
19. A. Salem and B. Alghamdi, Multi-strip and multi-point boundary conditions for fractional Langevin equation. Fractal and Fractional 4, 18, (2020). https://doi.org/10.3390/fractalfract4020018
20. A. Salem and B. Alghamdi, Multi-point and anti-periodic conditions for generalized Langevin equation with two fractional orders. Fractal and Fractional 3, 51,(2019) . https://doi.org/10.3390/fractalfract3040051
21. G. V. Smirnov, Introduction to the Theory of Differential Inclusions. Graduate Studies in Mathematics, American Mathematical Society vol 41, Providence, RI, USA, (2002). https://doi.org/10.1090/gsm/041
22. J. Yang, J. C. Ma, S. Zhao, and Y. Ge, Fractional multi-point boundary value problem of fractional differential equations. Mathematics in Practice and Theory 41, 188-194, (2011) .
23. Y. Zhou, Basic Theory of Fractional Differential Equations. Xiangtan University, China, 2014. https://doi.org/10.1142/9069
24. Z. Zhou, Y. Qiao, Solutions for a class of fractional Langevin equations with integral and anti-periodic boundary conditions. Boundary Value Problems 2018 (2018). https://doi.org/10.1186/s13661-018-1070-3
25. A. Lachouri, M. S. Abdo, A. Ardjouni, B. Abdalla and T. Abdeljawad. On a class of differential inclusions in the frame of generalized Hilfer fractional derivative. AIMS Mathematics, 7(3), 3477-3493, (2022). https://doi.org/10.3934/math.2022193
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2022-12-27
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