On a partial Hadamard fractional integral inclusion
Discussiones Mathematicae. Differential Inclusions, Control and Optimization, Tome 36 (2016) no. 2, pp. 141-153.

Voir la notice de l'article provenant de la source Library of Science

We study a class of nonconvex Hadamard fractional integral inclusions and we establish some Filippov type existence results.
Keywords: Hadamard fractional derivative, integral inclusion, decomposable set
@article{DMDICO_2016_36_2_a1,
     author = {Cernea, Aurelian},
     title = {On a partial {Hadamard} fractional integral inclusion},
     journal = {Discussiones Mathematicae. Differential Inclusions, Control and Optimization},
     pages = {141--153},
     publisher = {mathdoc},
     volume = {36},
     number = {2},
     year = {2016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMDICO_2016_36_2_a1/}
}
TY  - JOUR
AU  - Cernea, Aurelian
TI  - On a partial Hadamard fractional integral inclusion
JO  - Discussiones Mathematicae. Differential Inclusions, Control and Optimization
PY  - 2016
SP  - 141
EP  - 153
VL  - 36
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DMDICO_2016_36_2_a1/
LA  - en
ID  - DMDICO_2016_36_2_a1
ER  - 
%0 Journal Article
%A Cernea, Aurelian
%T On a partial Hadamard fractional integral inclusion
%J Discussiones Mathematicae. Differential Inclusions, Control and Optimization
%D 2016
%P 141-153
%V 36
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DMDICO_2016_36_2_a1/
%G en
%F DMDICO_2016_36_2_a1
Cernea, Aurelian. On a partial Hadamard fractional integral inclusion. Discussiones Mathematicae. Differential Inclusions, Control and Optimization, Tome 36 (2016) no. 2, pp. 141-153. http://geodesic.mathdoc.fr/item/DMDICO_2016_36_2_a1/

[1] S. Abbas, E. Alaidarous, W. Albarakati and M. Benchohra, Upper and lower solutions method for partial Hadamard fractional integral equations and inclusions, Discuss. Math. DICO 35 (2015), 105-122. doi: 10.7151/dmdico.1172

[2] S. Abbas, W. Albarakati, M. Benchohra and J. Henderson, Existence and Ulam stabilities for Hadamard fractional integral equations with random effects, Electronic J. Diff. Equations 2016 (2016), 1-12.

[3] S. Abbas, M. Benchohra and J. Henderson, Partial Hadamard fractional integral equations, Adv. Dynam. Systems Appl 10 (2015), 97-107.

[4] D. Baleanu, K. Diethelm, E. Scalas and J.J. Trujillo, Fractional Calculus: Models and Numerical Methods, World Scientific, Singapore, 2012, 10.1142/8180.

[5] A. Bressan and G. Colombo, Extensions and selections of maps with decomposable values, Studia Math 90 (1988), 69-86.

[6] C. Castaing and M. Valadier, Convex Analysis and Measurable Multifunctions (Springer, Berlin,1977). doi: 10.1007/BFb0087685

[7] A. Cernea, On the existence of solutions for nonconvex fractional hyperbolic differential inclusions, Commun. Math. Analysis 9 (2010), 109-120.

[8] A. Cernea, On an integro-differential inclusion of fractional order, Diff. Equations Dynam. Systems 21 (2013), 225-236. doi: 10.1007/s12591-012-0148-0

[9] A. Cernea, Filippov lemma for a class of Hadamard-type fractional differential inclusions, Fractional Calculus Appl. Analysis 18 (2015), 163-171. doi: 10.1515/fca-2015-0011

[10] A.F. Filippov, Classical solutions of differential equations with multivalued right hand side, SIAM J. Control 5 (1967), 609-621. doi: 10.1137/0305040

[11] J. Hadamard, Essai sur l'etude des fonctions donnees par leur development de Taylor, J. Math. Pures Appl. 8 (1892), 101-186.

[12] A. Kilbas, H.M. Srivastava and J.J. Trujillo, Theory and Applications of Fractional Differential Equations (Elsevier, Amsterdam, 2006).

[13] A. Kilbas, Hadamard-type fractional calculus, J. Korean Math. Soc. 38 (2001), 1191-1204.

[14] M. Kisielewicz, Differential Inclusions and Optimal Control (Kluwer, Dordrecht, 1991).

[15] I. Podlubny, Fractional Differential Equations (Academic Press, San Diego, 1999).