Geodesic
Upper and lower solutions method for partial discontinuous fractional differential inclusions with not instantaneous impulses
Discussiones Mathematicae. Differential Inclusions, Control and Optimization, Tome 36 (2016) no. 2, pp. 155-179.

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In this paper, we use the upper and lower solutions method combined with a fixed point theorem for multivalued maps in Banach algebras due to Dhage for investigations of the existence of solutions of a class of discontinuous partial differential inclusions with not instantaneous impulses. Also, we study the existence of extremal solutions under Lipschitz, Carath´eodory and certain monotonicity conditions
Keywords: fractional differential inclusion, left-sided mixed Riemann-Liouville integral, Caputo fractional order derivative, upper solution, lower solution, extremal solution, fixed point, Banach algebras, not instantaneous impulses 
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Abbas, Saïd; Benchohra, Mouffak; Abdalla Darwish, Mohamed. Upper and lower solutions method for partial discontinuous fractional differential inclusions with not instantaneous impulses. Discussiones Mathematicae. Differential Inclusions, Control and Optimization, Tome 36 (2016) no. 2, pp. 155-179. http://geodesic.mathdoc.fr/item/DMDICO_2016_36_2_a2/

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