On the solutions of a coupled system of proportional fractional differential inclusions of Hilfer type
Keywords:
differential inclusion, fractional derivative, boundary value problemAbstract
A multi-point and integro-multi-strip boundary value problem associated to a Hilfer type coupled system of fractional differential inclusions is studied. The existence of solutions is established in the case when the set-valued maps has nonconvex values.
References
J. P. Aubin, H. Frankowska: Set-valued Analysis, Birkh˝auser, Basel (1990).
D. B˘aleanu, K. Diethelm, E. Scalas and J. J. Trujillo: Fractional Calculus Models and Numerical Methods,World Scientific, Singapore (2012).
A. Cernea: Existence of solutions for some coupled systems of fractional differential inclusions, Mathematics, 8 (700) (2020), 1–10.
A. Cernea: On some coupled systems of fractional differential inclusions, Fract. Differ. Calc., 11 (2021), 133–145.
A. Cernea: A note on a coupled system of Caputo-Fabrizio fractional differential inclusions, Ann. Commun. Math., 4 (2021), 190–195.
A. Cernea: A note on a coupled system of Hilfer fractional differential inclusions, Foundations, 2 (2022), 290–297.
A. Cernea: On a Hilfer type fractional integro-differential inclusion, Bull. Transilv. Univ. Bra¸sov Ser. III. Math. Comput. Sci., 16 (2023), 71–80.
A. Cernea: On a Hilfer generalized proportional fractional integro-differential inclusion, Proceedings of International Conference of Fractional Differentiation and its Applications ICFDA 2024, Bordeaux (France), to appear.
K. Diethelm: The Analysis of Fractional Differential Equations, Springer, Berlin (2010). [10] A. F. Filippov: Classical solutions of differential equations with multivalued right hand side, SIAM J. Control, 5 (1967), 609–621.
R. Hilfer: Applications of Fractional Calculus in Physics, World Scientific, Singapore (2000).
R. Hilfer, Y. Luchko and Z. Tomovski: Operational method for the solution of fractional differential equations with generalized Riemann-Liouville fractional derivative, Fract. Calc. Appl. Anal., 12 (2009), 299–318.
A. Kilbas, H. M. Srivastava and J. J. Trujillo: Theory and Applications of Fractional Differential Equations, Elsevier,
Amsterdam (2006).
I. Mallah, I. Ahmed, A. Akgul, F. Jarad and S. Alha: On ψ-Hilfer generalized proportional fractional operators, AIMS Mathematics, 7 (2021), 82–103.
K. Miller, B. Ross: An Introduction to the Fractional Calculus and Differential Equations, JohnWiley, New York (1993).
S. K. Ntouyas, B. Ahmad and J. Tariboon: Coupled systems of nonlinear proportional fractional differential equations of the Hilfer-type with multi-point and integro-multi-strip boundary conditions, Foundations, 2 (3) (2023), 241–259.
I. Podlubny: Fractional Differential Equations, Academic Press, San Diego (1999).
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2024 Aurelian Cernea
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
