Solving a system of Caputo-Hadamard fractional differential equations via Perov’s fixed point theorem

Nouar, Aziza Souad; Nisse, Khadidja; Beloul, Said

doi:10.2478/awutm-2025-0001

Abstract

In this study, we discuss the existence and the uniqueness of the solution to Caputo-Hadamard Cauchy problems for a system of fractional differential equations, by using Perov’s fixed point theorem. Finally, two examples are provided to illustrate our results.

References

H. H. Alsulami, S. K. Ntouyas, R. P. Agarwal, B. Ahmad, A. Alsaedi, A study of fractional-order coupled systems with a new concept of coupled non-separated boundary conditions, Bound. Value Probl. 2017 (2017), 68.
Search in Google Scholar Back to article
A. M. Bica, S. Mureşan, Approaching nonlinear Volterra neutral delay integro-differential equations with the Perov’s fixed point theorem, Fixed Point Theory 8 (2) (2007), 187-200.
Search in Google Scholar Back to article
M. Cvetković, V. Rakočević, Extensions of Perov theorem, Carpathian J. Math. 31 (2015), 181-188.
Search in Google Scholar Back to article
N. Fabiano, Z. Kadelburg, N. Mirkov, S. Radenović, Solving fractional differential equations using fixed point results in generalized metric spaces of Perov’s type, TWMS J. Appl. Eng. Math. 13 (3) (2023), 880-890.
Search in Google Scholar Back to article
A. Granas, J. Dugundji, Fixed point theory, Springer-Verlag, New York, 2003.
Search in Google Scholar Back to article
Ch. Guendouz, J. E. Lazreg, J. J. Nieto, A. Ouahab, Existence and compactness results for a system of fractional differential equations, J. Funct. Spaces 2020 (2020), 5735140.
Search in Google Scholar Back to article
L. Guran, M. - F. Bota, A. Naseem, Fixed point problems on generalized metric spaces in Perov’s sense, Symmetry 12 (2020), 856.
Search in Google Scholar Back to article
A. Hamrouni, S. Beloul, A. Aissaoui, Existence of solutions for boundary value problems of fractional integro-differential equations with integral boundary conditions on Banach spaces, Nonlinear Stud. 26 (3) (2019), 693-701.
Search in Google Scholar Back to article
A. Hamrouni, S. Beloul, Existence of solutions for boundary value problems of fractional integro-differential equations with integral boundary conditions on Banach spaces, Mathematica 65 (2023), 249-262.
Search in Google Scholar Back to article
R. Hilfer, Applications of fractional calculus in physics, World Scientific, Singapore, 2000.
Search in Google Scholar Back to article
F. Jarad, T. Abdeljawad, D. Baleanu, Caputo-type modification of the Hadamard fractional derivatives, Adv. Difference Equ. 2012 (2012), 142.
Search in Google Scholar Back to article
A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and applications of fractional differential equations, Elsevier B.V., Amsterdam, 2006.
Search in Google Scholar Back to article
Z. Malki, F. Barhoun, A. Ouahab, System of boundary random fractional differential equations via Hadamard derivative, Ann. Univ. Paedagog. Crac. Stud. Math. 20 (2021), 17-41.
Search in Google Scholar Back to article
S. Mureşan, L. F. Iambor, O. Bazighifan, New applications of Perov’s fixed point theorem, Mathematics 10 (2022), 4597.
Search in Google Scholar Back to article
M. Nazam, H. Ahmad, M. Waheed, S. Askar, On the Perov’s type (β, F)-contraction principle and an application to delay integro-differential problem, AIMS Math. 8 (10) (2023), 23871-23888.
Search in Google Scholar Back to article
O. M. Nica, G. Infante, R. Precup, Existence results for systems with coupled nonlocal initial conditions, Nonlinear Anal., Theory Methods Appl. 94 (2014), 231-242.
Search in Google Scholar Back to article
A. Novac, R. Precup, Perov type results in gauge spaces and their applications to integral systems on semi-axis, Math. Slovaca 64 (2014), 961-972.
Search in Google Scholar Back to article
A. I. Perov, A. V. Kibenko, On a certain general method for investigation of boundary value problems, Izv. Akad. Nauk SSSR Ser. Mat. 30 (1966), 249-264.
Search in Google Scholar Back to article
R. Precup, The role of matrices that are convergent to zero in the study of semilinear operator systems, Math. Comput. Modelling 49 (3-4) (2009), 703-708.
Search in Google Scholar Back to article
R. S. Varga, Matrix iterative analysis, Springer Science & Business Media, 1999.
Search in Google Scholar Back to article
P. Zhang, X. Hao, Existence and uniqueness of solutions for a class of nonlinear integrodifferential equations on unbounded domains in Banach spaces, Adv. Difference Equ. 2018 (2018), 247.
Search in Google Scholar Back to article

Solving a system of Caputo-Hadamard fractional differential equations via Perov’s fixed point theorem

Abstract

Paradigm

My account