Abstract
We study a Darboux problem associated to a fractional hyperbolic integro-differential inclusion defined by Caputo-Katugampola fractional derivative and we prove several existence results for this problem.
Highlights
We study a Darboux problem associated to a fractional hyperbolic integro-differential inclusion defined by Caputo-Katugampola fractional derivative and we prove several existence results for this problem
In the last years one may see a strong development of the theory of differential equations and inclusions of fractional order ( [2, 7, 11,12,13] etc.)
The main reason is that fractional differential equations are very useful tools in order to model many physical phenomena
Summary
In the last years one may see a strong development of the theory of differential equations and inclusions of fractional order ( [2, 7, 11,12,13] etc.). In some recent papers [1, 15], several qualitative properties of solutions of fractional differential equations defined by Caputo-Katugampola derivative were obtained. Our second theorem allows to deduce a continuous selection of the solution set of the problem considered.
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