We study a class of nonconvex Hadamard fractional integral inclusions and we establish some Filippov type existence results.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1188, author = {Aurelian Cernea}, title = {On a partial Hadamard fractional integral inclusion}, journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization}, volume = {36}, year = {2016}, pages = {141-153}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1188} }
Aurelian Cernea. On a partial Hadamard fractional integral inclusion. Discussiones Mathematicae, Differential Inclusions, Control and Optimization, Tome 36 (2016) pp. 141-153. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1188/
[000] [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
[001] [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.
[002] [3] S. Abbas, M. Benchohra and J. Henderson, Partial Hadamard fractional integral equations, Adv. Dynam. Systems Appl 10 (2015), 97-107.
[003] [4] D. Baleanu, K. Diethelm, E. Scalas and J.J. Trujillo, Fractional Calculus: Models and Numerical Methods, World Scientific, Singapore, 2012, 10.1142/8180.
[004] [5] A. Bressan and G. Colombo, Extensions and selections of maps with decomposable values, Studia Math 90 (1988), 69-86.
[005] [6] C. Castaing and M. Valadier, Convex Analysis and Measurable Multifunctions (Springer, Berlin,1977). doi: 10.1007/BFb0087685
[006] [7] A. Cernea, On the existence of solutions for nonconvex fractional hyperbolic differential inclusions, Commun. Math. Analysis 9 (2010), 109-120.
[007] [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
[008] [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
[009] [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
[010] [11] J. Hadamard, Essai sur l'etude des fonctions donnees par leur development de Taylor, J. Math. Pures Appl. 8 (1892), 101-186.
[011] [12] A. Kilbas, H.M. Srivastava and J.J. Trujillo, Theory and Applications of Fractional Differential Equations (Elsevier, Amsterdam, 2006).
[012] [13] A. Kilbas, Hadamard-type fractional calculus, J. Korean Math. Soc. 38 (2001), 1191-1204.
[013] [14] M. Kisielewicz, Differential Inclusions and Optimal Control (Kluwer, Dordrecht, 1991).
[014] [15] I. Podlubny, Fractional Differential Equations (Academic Press, San Diego, 1999).