System of boundary random fractional differential equations via Hadamard derivative

Zakaria Malki; Farida Berhoun; Abdelghani Ouahab

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica (2021)

  • Volume: 20, page 17-41
  • ISSN: 2300-133X

Abstract

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We study the existence of solutions for random system of fractional differential equations with boundary nonlocal initial conditions. Our approach is based on random fixed point principles of Schaefer and Perov, combined with a vector approach that uses matrices that converge to zero. We prove existence and uniqueness results for these systems. Some examples are presented to illustrate the theory.

How to cite

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Zakaria Malki, Farida Berhoun, and Abdelghani Ouahab. "System of boundary random fractional differential equations via Hadamard derivative." Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica 20 (2021): 17-41. <http://eudml.org/doc/296829>.

@article{ZakariaMalki2021,
abstract = {We study the existence of solutions for random system of fractional differential equations with boundary nonlocal initial conditions. Our approach is based on random fixed point principles of Schaefer and Perov, combined with a vector approach that uses matrices that converge to zero. We prove existence and uniqueness results for these systems. Some examples are presented to illustrate the theory.},
author = {Zakaria Malki, Farida Berhoun, Abdelghani Ouahab},
journal = {Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica},
keywords = {Random fractional differential equation; Hadamard fractional differential equation; existence; fixed point; vector metric space},
language = {eng},
pages = {17-41},
title = {System of boundary random fractional differential equations via Hadamard derivative},
url = {http://eudml.org/doc/296829},
volume = {20},
year = {2021},
}

TY - JOUR
AU - Zakaria Malki
AU - Farida Berhoun
AU - Abdelghani Ouahab
TI - System of boundary random fractional differential equations via Hadamard derivative
JO - Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica
PY - 2021
VL - 20
SP - 17
EP - 41
AB - We study the existence of solutions for random system of fractional differential equations with boundary nonlocal initial conditions. Our approach is based on random fixed point principles of Schaefer and Perov, combined with a vector approach that uses matrices that converge to zero. We prove existence and uniqueness results for these systems. Some examples are presented to illustrate the theory.
LA - eng
KW - Random fractional differential equation; Hadamard fractional differential equation; existence; fixed point; vector metric space
UR - http://eudml.org/doc/296829
ER -

References

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  1. Abbas, Saïd, Mouffak Benchohra, and Gaston Mandata N’Guérékata. Topics in fractional differential equations. New York: Springer, 2012. 
  2. Bahya, Roummani, and Johnny Henderson, and Abdeghani Ouahab. "Existence and solution sets for systems of impulsive differential inclusions" Mem. Differ. Equ. Math. Phys. 82 (2021): 1-37. 
  3. Berrezoug, Halimi, and Johnny Henderson, and Abdelghani Ouahab. "Existence and uniqueness of solutions for a system of impulsive differential equations on the half-line." Journal of Nonlinear Functional Analysis 2017 (2017): Article ID 38. 
  4. Baleanu, Dumitru, Kai Diethelm, Enrico Scalas, Juan J. Trujillo. Fractional Calculus: Models and Numerical Methods. New York: World Scientific Publishing, 2012. 
  5. Bharucha-Reid, Albert Turner (eds.). Random Integral Equations. New York: Academic Press, 2012. 
  6. Nica, Octavia-Maria, Gennaro Infante, and Radu Precup. "Existence results for systems with coupled nonlocal initial conditions." Nonlinear Anal. 94 (2014): 231-242. 
  7. Deng, Ji Qin, and Lifeng Ma. "Existence and uniqueness of solutions of initial value problems for nonlinear fractional differential equations." Appl. Math. Lett. 23, no. 6 (2010): 676-680. 
  8. Graef, John R., Johnny Henderson, and Abdelghani Ouahab. Topological Methods for Differential Equations and Inclusions. Monographs and Research Notes in Mathematics Series Profile. Boca Raton-London-New York: CRC Press, 2019. 
  9. Graef, John R. et al. "Existence results for systems of second-order impulsive differential equations." Acta Math. Univ. Comenian. (N.S.) 88, no. 1 (2019): 51-66. 
  10. Jarad, Fahd, Thabet Abdeljawad, and Dumitru I. Baleanu. "Caputo-type modification of the Hadamard fractional derivatives." Adv. Difference Equ. (2012): 142. 
  11. Kilbas, Anatoly Aleksandrovich, Hari Mohan Srivastava, and Juan J. Trujillo. Theory and Applications of Fractional Differential Equations. Vol. 204 of North-Holland Mathematics Studies. Amsterdam: Elsevier Science B.V, 2006. 
  12. Ladde, Gangaram Shivlingappa and Vangipuram Lakshmikantham. Random Differential Inequalities. New York: Academic Press, 1980. 
  13. Lakshmikantham, Vangipuram. "Theory of fractional functional differential equations." Nonlinear Anal. 69, no. 10 (2008): 3337-3343. 
  14. Lakshmikantham, Vangipuram, and Aghalaya S. Vatsala. "Theory of fractional differential inequalities and applications." Commun. Appl. Anal. 11, no. 3-4 (2007): 395-402. 
  15. Lakshmikantham, Vangipuram, and Aghalaya S. Vatsala. "Basic theory of fractional differential equations." Nonlinear Anal. 69, no. 8 (2008): 2677-2682. 
  16. Lupulescu, Vasile, and S.K. Ntouyas. "Random fractional differential equations." Int. Electron. J. Pure Appl. Math. 4, no. 2 (2012): 119-136. 
  17. Lupulescu, Vasile, Donal O’Regan, and Ghaus ur Rahman. "Existence results for random fractional differential equations." Opuscula Math. 34, no. 4 (2014): 813-825. 
  18. Nica, Octavia-Maria. "Existence results for second order three-point boundary value problems." Differ. Equ. Appl. 4, no. 4 (2012): 547-570. 
  19. Nica, Octavia-Maria. "Initial-value problems for first-order differential systems with general nonlocal conditions." Electron. J. Differential Equations 2012 (2012): No. 74. 
  20. Nica, Octavia-Maria, and Radu Precup. "On the nonlocal initial value problem for first order differential systems." Stud. Univ. Babes-Bolyai Math. 56, no. 3 (2011): 113-125. 
  21. Papageorgiou, Nikolaos Socrates. "Random fixed point theorems for measurable multifunctions in Banach spaces." Proc. Amer. Math. Soc. 97, no. 3 (1986): 507-514. 
  22. Precup, Radu. "The role of matrices that are convergent to zero in the study of semilinear operator systems." Math. Comput. Modelling 49, no. 3-4 (2009): 703-708. 
  23. Sinacer, Moulay Larbi, Juan J. Nieto Roig, and Abdelghani Ouahab. "Random fixed point theorem in generalized Banach space and applications." Random Oper. Stoch. Equ. 24, no. 2 (2016): 93-112. 
  24. Tariboon, Jessada, Sotiris K. Ntouyas, and Chatthai Thaiprayoon. "Nonlinear Langevin equation of Hadamard-Caputo type fractional derivatives with nonlocal fractional integral conditions." Adv. Math. Phys. (2014): Art. ID 372749. 
  25. Tsokos, Chris Peter, and William Jowayne Padgett. Random Integral Equations with Applications to Life Sciences and Engineering. New York: Academic Press, 1974. 
  26. Varga, Richard S. Matrix Iterative Analysis. Vol. 27 of Springer Series in Computational Mathematics. Berlin: Springer-Verlag, 2000. 

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