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
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top- Abbas, Saïd, Mouffak Benchohra, and Gaston Mandata N’Guérékata. Topics in fractional differential equations. New York: Springer, 2012.
- 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.
- 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.
- Baleanu, Dumitru, Kai Diethelm, Enrico Scalas, Juan J. Trujillo. Fractional Calculus: Models and Numerical Methods. New York: World Scientific Publishing, 2012.
- Bharucha-Reid, Albert Turner (eds.). Random Integral Equations. New York: Academic Press, 2012.
- Nica, Octavia-Maria, Gennaro Infante, and Radu Precup. "Existence results for systems with coupled nonlocal initial conditions." Nonlinear Anal. 94 (2014): 231-242.
- 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.
- 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.
- 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.
- Jarad, Fahd, Thabet Abdeljawad, and Dumitru I. Baleanu. "Caputo-type modification of the Hadamard fractional derivatives." Adv. Difference Equ. (2012): 142.
- 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.
- Ladde, Gangaram Shivlingappa and Vangipuram Lakshmikantham. Random Differential Inequalities. New York: Academic Press, 1980.
- Lakshmikantham, Vangipuram. "Theory of fractional functional differential equations." Nonlinear Anal. 69, no. 10 (2008): 3337-3343.
- Lakshmikantham, Vangipuram, and Aghalaya S. Vatsala. "Theory of fractional differential inequalities and applications." Commun. Appl. Anal. 11, no. 3-4 (2007): 395-402.
- Lakshmikantham, Vangipuram, and Aghalaya S. Vatsala. "Basic theory of fractional differential equations." Nonlinear Anal. 69, no. 8 (2008): 2677-2682.
- Lupulescu, Vasile, and S.K. Ntouyas. "Random fractional differential equations." Int. Electron. J. Pure Appl. Math. 4, no. 2 (2012): 119-136.
- Lupulescu, Vasile, Donal O’Regan, and Ghaus ur Rahman. "Existence results for random fractional differential equations." Opuscula Math. 34, no. 4 (2014): 813-825.
- Nica, Octavia-Maria. "Existence results for second order three-point boundary value problems." Differ. Equ. Appl. 4, no. 4 (2012): 547-570.
- Nica, Octavia-Maria. "Initial-value problems for first-order differential systems with general nonlocal conditions." Electron. J. Differential Equations 2012 (2012): No. 74.
- 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.
- Papageorgiou, Nikolaos Socrates. "Random fixed point theorems for measurable multifunctions in Banach spaces." Proc. Amer. Math. Soc. 97, no. 3 (1986): 507-514.
- 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.
- 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.
- 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.
- Tsokos, Chris Peter, and William Jowayne Padgett. Random Integral Equations with Applications to Life Sciences and Engineering. New York: Academic Press, 1974.
- Varga, Richard S. Matrix Iterative Analysis. Vol. 27 of Springer Series in Computational Mathematics. Berlin: Springer-Verlag, 2000.