Abstract
In this manuscript, we study the sufficient conditions for controllability for fractional functional integro-differential systems involving the Caputo fractional derivative of order in Banach spaces. Our main approach is based on fractional calculus, the properties of characteristic solution operators, Monch’s fixed point theorem via measures of noncompactness. Particularly, these results are under some weakly compactness conditions. An example is presented in the end to show the applications of the obtained abstract results. MSC:26A33, 93B05, 47H08, 47H10.
Highlights
The theory of fractional differential and integral equations have been proved to be valuable tools and effective in the modeling of many phenomena in various fields of engineering and scientific disciplines such as physics, chemistry, biology, control theory, signal and image processing, biophysics, blood flow phenomena, aerodynamics and so on
The authors Wang and Zhou [ ] found some conditions guaranteeing the complete controllability of fractional evolution systems without assuming the compactness of characteristic solution operators by means of the Mönch fixed point technique and the measures of noncompactness
In Section, we establish some sufficient conditions for controllability of fractional integro-differential evolution systems with infinite delay
Summary
The theory of fractional differential and integral equations have been proved to be valuable tools and effective in the modeling of many phenomena in various fields of engineering and scientific disciplines such as physics, chemistry, biology, control theory, signal and image processing, biophysics, blood flow phenomena, aerodynamics and so on. The authors Wang and Zhou [ ] found some conditions guaranteeing the complete controllability of fractional evolution systems without assuming the compactness of characteristic solution operators by means of the Mönch fixed point technique and the measures of noncompactness. Wang et al [ ] established two sufficient conditions for nonlocal controllability for fractional evolution systems These theorems guarantee the effectiveness of controllability results under some weakly noncompactness conditions. From the above literature survey, to our knowledge, controllability of fractional functional integro-differential systems with infinite delay by using Mönch’s fixed point theorem via MNC properties and an abstract phase space have not been studied fully. In Section , we establish some sufficient conditions for controllability of fractional integro-differential evolution systems with infinite delay.
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