Abstract
We establish some Filippov type existence theorems for solutions of fractional semilinear differential inclusions involving Caputo’s fractional derivative in Banach spaces.
Highlights
Differential equations with fractional order have recently proved to be strong tools in the modelling of many physical phenomena
As a consequence there was an intensive development of the theory of differential equations of fractional order ([21, 22, 24] etc.)
Applied problems require definitions of fractional derivative allowing the utilization of physically interpretable initial conditions
Summary
Differential equations with fractional order have recently proved to be strong tools in the modelling of many physical phenomena. We recall that for a first order differential inclusion defined by a lipschitzian set-valued map with nonconvex values Filippov’s theorem ([17]) consists in proving the existence of o solution starting from a given ”almost” solution. We prove the existence of solutions continuously depending on a parameter for problem (1.1) This result may be interpreted as a continuous variant of Filippov’s theorem for problem (1.1). The key tool in the proof of this theorem is a result of Bressan and Colombo ([4]) concerning the existence of continuous selections of lower semicontinuous multifunctions with decomposable values This result allows to obtain a continuous selection of the solution set of the problem considered. The paper is organized as follows: in Section 2 we briefly recall some preliminary results that we will use in the sequel and in Section 3 we prove the main results of the paper
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Electronic Journal of Qualitative Theory of Differential Equations
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
