Coupled systems of conformable fractional differential equations
Abstract
This paper deals with some existence of solutions for some classes of coupled systems of conformable fractional differential equations with initial and boundary conditions in Banach and Fréchet spaces. Our results are based on some fixed point theorems. Some illustrative examples are presented in the last section.
Full Text:
PDFReferences
S. Abbas, M. Benchohra, J.R. Graef, J. Henderson, Implicit fractional differential and integral equations. Existence and stability, De Gruyter, Berlin, 2018.
S. Abbas, M. Benchohra, J.E. Lazreg, J.J. Nieto, Y. Zhou, Fractional Differential Equations and Inclusions: Classical and Advanced Topics, World Scienti_c, Hackensack, NJ, 2023.
T. Abdeljawad, On conformable fractional calculus, J. Comput. Appl. Math. 279 (2015), 57-66.
T. Abdeljawad, Q.M. Al-Mdallal, F. Jarad, Fractional logistic models in the frame of fractional operators generated by conformable derivatives. Chaos Solitons Fractals 119 (2019), 94-101.
S. Aibout, S. Abbas, M. Benchohra, M. Bohner, A coupled Caputo-Hadamard fractional differential system with multipoint boundary conditions, Dynamics Con. Discrete Impul. Sys. Series A: Math. Anal. 29 (2022), 191-209.
S. Alfaqeih, I. Kayijuka, Solving system of conformable fractional differential equations by conformable double Laplace decomposition method. J. Partial Differ. Equ. 33 (2020), no. 3, 275-290.
H. Batarfi, J. Losada, J.J. Nieto, W. Shammakh, Three-point boundary value problems for conformable fractional differential equations, J. Funct. Spaces 70 (2015), 63-83.
M. Chohri, S. Bouriah, A. Salim, M. Benchohra, On nonlinear periodic problems with Caputo's exponential fractional derivative, ATNAA. 7 (2023), 103-120. https://doi.org/10.31197/atnaa.1130743
C. Derbazi, H. Hammouche, A. Salim, M. Benchohra, Weak solutions for fractional Langevin equations involving two fractional orders in Banach spaces, Afr. Mat. 34 (2023). https://doi.org/10.1007/s13370-022-01035-3
A. El-Ajou, A modification to the conformable fractional calculus with some applications, Alexandria Engineering J. 59 (2020), 2239-2249.
A. Granas, J. Dugundji, Fixed Point Theory, Springer, New York, 2005.
J. R.Graef, J. Henderson, A. Ouahab, Impulsive Diferential Inclusions. A Fixed Point Approch, De Gruyter, Berlin/Boston, 2013.
M.A. Hammad, R. Khalil, Abels formula and Wronskian for conformable fractional differential equations. Int. J. Differ. Equ. Appl. 13(3) (2014), 177-183.
A. Harir, S. Melliani, L.S. Chadli, Fuzzy Conformable Fractional Differential Equations. Int. J. Differ. Equ. 2021 (2021), Art. ID 6655450.
N. Kadkhoda, H. Jafari, An analytical approach to obtain exact solutions of some space-time conformable fractional differential equations. Adv. Difference Equ. 2019 (2019), Art. 428.
R. Khalil, M.A. AL Horani, M. Yousef, M. Sababheh, A new efinition of fractional derivative, J. Comput. Appl. Math. 264 (2014), 65-70.
A.A. Kilbas, H.M. Srivastava, J. J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier Science B.V., Amsterdam, 2006.
S. Krim, A. Salim, S. Abbas, M. Benchohra, On implicit impulsive conformable fractional differential equations with infinite delay in b-metric spaces, Rend. Circ. Mat. Palermo Series 2 72 (2023), 2579|2592. https://doi.org/10.1007/s12215-022-00818-8
S. Krim, A. Salim, S. Abbas, M. Benchohra, Functional k-generalized -Hilfer fractional differential equations in b-metric spaces, Pan-Amer. J. Math. 2 (2023). https://doi.org/10.28919/cprpajm/2-5
W. Rahou, A. Salim, J.E. Lazreg, M. Benchohra, Existence and stability results for impulsive implicit fractional differential equations with delay and Riesz-Caputo derivative, Mediterr. J. Math. 20 (2023), Art. 143. https://doi.org/10.1007/s00009-023-02356-8
M. Rehman, R.A. Khan, A note on boundary value problems for a coupled system of fractional differential equations, Compu. Math. Appl. 61 (2011), 2630-02637.
A. Salim, M. Benchohra, J.E. Lazreg, On implicit k-generalized -Hilfer fractional differential coupled systems with periodic conditions, Qual. Theory Dyn. Syst. 22 (2023). https://doi.org/10.1007/s12346-023-00776-1
S.G. Samko, A.A. Kilbas, O.I. Marichev, Fractional Integrals and Derivatives.Theory and Applications, Gordon and Breach, Amsterdam, 1987., Engl. Trans. from the Russian.
V.E. Tarasov, Fractional Dynamics: Application of Fractional Calculus to Dynamics of Particles, Fields and Media, Springer, Heidelberg, Beijing, 2010.
J.M.A. Toledano, T. Dominguez Benavides, G. Lopez Acedo, Measures of Noncompactness in Metric Fixed Point Theory, Birkhauser, Basel, 1997.
J. Wang, C. Bai, Antiperiodic boundary value problems for impulsive fractional functional differential equations via conformable derivative, J. Funct. Spaces 2018 (2018) Art. ID 7643123.
G. Xiao, J. Wang, Representation of solutions of linear conformable delay differential equations, Appl. Math. Lett. 117 (2021), 107088.
Y. Zhou, Basic Theory of Fractional Differential Equations, World Scientific, Singapore, 2014.
DOI: https://doi.org/10.52846/ami.v51i1.1750