Boundary value problems for Caputo-Hadamard fractional differential inclusions in Banach spaces
Archivum mathematicum, Tome 58 (2022) no. 4, pp. 227-240 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

In this article, we study the existence of solutions in a Banach space of boundary value problems for Caputo-Hadamard fractional differential inclusions of order $r \in (0,1]$.
In this article, we study the existence of solutions in a Banach space of boundary value problems for Caputo-Hadamard fractional differential inclusions of order $r \in (0,1]$.
DOI : 10.5817/AM2022-4-227
Classification : 26A33, 34A37
Keywords: fractional differential inclusion; Caputo-Hadamard fractional derivative; Mönch’s fixed point theorem; Kuratowski measure of noncompactness
@article{10_5817_AM2022_4_227,
     author = {Hammou, Amouria and Hamani, Samira and Henderson, Johnny},
     title = {Boundary value problems for {Caputo-Hadamard} fractional differential inclusions in {Banach} spaces},
     journal = {Archivum mathematicum},
     pages = {227--240},
     year = {2022},
     volume = {58},
     number = {4},
     doi = {10.5817/AM2022-4-227},
     mrnumber = {4529815},
     zbl = {07655745},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.5817/AM2022-4-227/}
}
TY  - JOUR
AU  - Hammou, Amouria
AU  - Hamani, Samira
AU  - Henderson, Johnny
TI  - Boundary value problems for Caputo-Hadamard fractional differential inclusions in Banach spaces
JO  - Archivum mathematicum
PY  - 2022
SP  - 227
EP  - 240
VL  - 58
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.5817/AM2022-4-227/
DO  - 10.5817/AM2022-4-227
LA  - en
ID  - 10_5817_AM2022_4_227
ER  - 
%0 Journal Article
%A Hammou, Amouria
%A Hamani, Samira
%A Henderson, Johnny
%T Boundary value problems for Caputo-Hadamard fractional differential inclusions in Banach spaces
%J Archivum mathematicum
%D 2022
%P 227-240
%V 58
%N 4
%U http://geodesic.mathdoc.fr/articles/10.5817/AM2022-4-227/
%R 10.5817/AM2022-4-227
%G en
%F 10_5817_AM2022_4_227
Hammou, Amouria; Hamani, Samira; Henderson, Johnny. Boundary value problems for Caputo-Hadamard fractional differential inclusions in Banach spaces. Archivum mathematicum, Tome 58 (2022) no. 4, pp. 227-240. doi: 10.5817/AM2022-4-227

[1] Adjabi, Y., Jarad, F., Baleanu, D., Abdeljawad, T.: On Cauchy problems with Caputo Hadamard fractional derivatives. J. Comput. Anal. Appl. 21 (4) (2016), 661–681. | MR

[2] Agarwal, R.P., Benchohra, M., Seba, D.: On the application of measure of noncom-pactness to the existence of solutions for fractional differential equations. Results Math. 55 (2009), 221–230. | DOI | MR

[3] Ahmad, B., Khan, R.A., Sivasundaram, S.: Generalized quasilinearization method for a first order differential equation with integral boundary condition. Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal. 12 (2) (2005), 289–296. | MR | Zbl

[4] Ahmad, B., Ntouyas, S.K.: Initial value problems for hybrid Hadamard fractional equations. Electron. J. Differential Equ. 2014 (161) (2014), 8 pp. | MR

[5] Akhmerov, R.R., Kamenski, M.I., Patapov, A.S., Rodkina, A.E., Sadovski, B.N.: Measures of noncompactness and condensing operators (Translated from the 1986 Russian original by A. Iacop), Operator theory: Advances and Applications. ranslated from the 1986 russian original by a. iacop), operator theory: advances and applications, vol. 55, Birkhäuser Verlag, Basel, 1992. | MR

[6] Aubin, J.P., Cellina, A.: Differential inclusions. Springer-Verlag, Berlin-Heidelberg, New York, 1984. | MR

[7] Aubin, J.P., Frankowska, H.: Set-valued analysis. Birkhäuser, Boston, 1990. | MR

[8] Banas, J., Goebel, K.: Measure of noncompactness in Banach spaces. Lecture Notes in Pure and Appl. Math., Marcel Dekker, New York, 1980. | MR

[9] Belarbi, A., Benchohra, M.: Existence results for nonlinear boundary-value problems with integral boundary conditions. Electron. J. Differential Equ. 6 (2005), 1–10. | MR

[10] Benchohra, M., Hamani, S.: Boundary value problems for differential inclusions with fractional order. Discuss. Math. Differ. Incl. Control Optim. 28 (2008), 147–164. | DOI | MR | Zbl

[11] Benchohra, M., Hamani, S.: Nonlinear boundary value problems for differential inclusions with Caputo fractional derivative. Topol. Methods Nonlinear Anal. 32 (1) (2008), 115–130. | MR | Zbl

[12] Benchohra, M., Henderson, J., Seba, D.: Measure of noncompactness and fractional differential equations in Banach spaces. Commun. Appl. Anal. 12 (2008), 419–428. | MR

[13] Benchohra, M., Henderson, J., Seba, D.: Measure of noncompactness and fractional andhyperbolic partial fractional differential equations in Banach space. PanAmer. Math. J. 20 (2010), 27–37. | MR

[14] Benchohra, M., Henderson, J., Seba, D.: Boundary value problems for fractional differential inclusions in Banach space. Fract. Differ. Calc. 2 (2012), 99–108. | MR

[15] Benhamida, W., Hamani, S.: Measure of noncompactness and Caputo-Hadamard fractional differantial equations in Banach spaces. Eur. Bull. Math. 1 (3) (2018), 98–103.

[16] Benhamida, W., Hamani, S., Henderson, J.: Boundary value problems for Caputo-Hadamard fractional differential equations. Adv. Theor. Nonlinear Anal. Appl. 2 (3) (2018), 138–145. | MR

[17] Brykalov, S.A.: A second order nonlinear problem with two-point and integral boundary conditions. Georgian Math. J. 1 (1994), 243–249. | DOI | MR | Zbl

[18] Butzer, P.L., Kilbas, A.A., Trujillo, J.J.: Composition of Hadamard-type fractional integration operators and the semigroup property. J. Math. Anal. Appl. 269 (2002), 387–400. | DOI | MR

[19] Butzer, P.L., Kilbas, A.A., Trujillo, J.J.: Fractional calculus in the Mellin setting and Hadamard-type fractional integrals. J. Math. Anal. Appl. 269 (2002), 1–27. | DOI | MR | Zbl

[20] Butzer, P.L., Kilbas, A.A., Trujillo, J.J.: Mellin transform analysis and integration by parts for Hadamard-type fractional integrals. J. Math. Anal. Appl. 270 (2002), 1–15. | DOI | MR | Zbl

[21] Deimling, .K.: Multivalued differential equations. Walter De Gruyter, Berlin-New York, 1992. | MR

[22] Denche, M., Marhoune, A.L.: High order mixed-type differential equations with weighted integral boundary conditions. Electron. J. Differential Equ. 2000 (60) (2000), 1–10. | MR

[23] Diethelm, K., Freed, A.D.: On the solution of nonlinear fractional order differential equations used in the modeling of viscoplasticity. Scientifice Computing in Chemical Engineering II-Computational Fluid Dynamics, Reaction Engineering and Molecular Properties (Keil, F., Mackens, W., Voss, H., Werther, J., eds.), Springer-Verlag, Heidelberg, 1999, pp. 217–224. | MR

[24] Gallardo, J.M.: Second order differential operators with integral boundary conditions and generation of semigroups. Rocky Mountain J. Math. 30 (2000), 1265–1292. | MR

[25] Gambo, Y.Y., Jarad, F., Baleanu, D., Abdeljawad, T.: On Caputo modification of the Hadamard fractional derivatives. Adv. Difference Equ. 2014 (10) (2014), 12 pp. | MR

[26] Gaul, L., Klein, P., Kempfle, S.: Damping description involving fractional operators. Mech. Systems Signal Processing 5 (1991), 81–88. | DOI

[27] Glockle, W.G., Nonnenmacher, T.F.: A fractional calculus approach of self-similar protein dynamics. Biophys. J. 68 (1995), 46–53. | DOI

[28] Hadamard, J.: Essai sur l’étude des fonctions donnees par leur development de Taylor. J. Math. Pure Appl. 8 (1892), 101–186.

[29] Hilfer, R.: Applications of fractional calculus in physics. World Scientific, Singapore, 2000. | MR | Zbl

[30] Jarad, F., Abdeljawad, T., Baleanu, D.: Caputo-type modification of the Hadamard fractional derivatives. Adv. Difference Equ. 2012 (142) (2012), 8 pp. | MR

[31] Karakostas, G.L., Tsamatos, P.Ch.: Multiple positive solutions of some Fredholm integral equations arisen from nonlocal boundary value problems. Electron. J. Differential Equ. 2002 (30) (2002), 1–17. | MR

[32] Khan, R. A.: The generalized method of quasilinearization and nonlinear boundary value problems with integral boundary conditions. Electron. J. Qual. Theory Differ. Equ. 2003 (10) (2003), 1–15. | DOI | MR | Zbl

[33] Kilbas, A.A.: Hadamard-type fractional calculus. J. Korean Math. Soc. 38 (6) (2001), 1191–1204. | MR

[34] Kilbas, A.A., Srivastava, H.M., Trujillo, J.J.: Theory and applications of fractional differential equations. North-Holland Math. Studies, Elsevier Science B.V., Amsterdam, 2006. | MR

[35] Klimek, M.: Sequential fractional differential equations with Hadamard derivative. Commun. Nonlinear Sci. Numer. Simul. 16 (12) (2011), 4689–4697. | DOI | MR

[36] Krall, A.M.: The adjoint of a differential operator with integral boundary conditions. Proc. Amer. Math. Soc. 16 (1965), 738–742. | DOI | MR

[37] Lomtatidze, A., Malaguti, L.: On a nonlocal boundary value problems for second order nonlinear singular differential equations. Georgian Math. J. 7 (2000), 133–154. | DOI | MR

[38] Mainardi, F.: Fractional calculus: Some basic problems in continuum and statistical mechanics. Fractals and Fractional Calculus in Continuum Mechanics (Carpinteri, A., Mainardi, F., eds.), Springer-Verlag, Wien, 1997, pp. 291–348. | MR

[39] Metzler, F., Schick, W., Kilian, H.G., Nonnenmacher, T.F.: Relaxation in filled polymers: A fractional calculus approach. J. Chem. Phys. 103 (1995), 7180–7186. | DOI

[40] Miller, K.S., Ross, B.: An introduction to the fractional calculus and differential equations. John Wiley, New York, 1993. | MR

[41] Oldham, K.B., Spanier, J.: The fractional calculus. Academic Press, New York, London, 1974. | MR

[42] O’Regan, D., Precup, R.: Fixed point theorems for set-valued maps and existence prin-ciples for integral inclusions. J. Math. Anal. Appl. 245 (2000), 594–612. | DOI | MR

[43] Thiramanus, P., Ntouyas, S.K., Tariboon, J.: xistence and uniqueness results for Hadamard-type fractional differential equations with nonlocal fractional integral boundary conditions. Abstr. Appl. Anal. 2014 (2014), 9 pp., Art. ID 902054. | MR

Cité par Sources :