APPROXIMATE CONTROLLABILITY FOR FRACTIONAL DIFFERENTIAL EQUATIONS OF SOBOLEV TYPE VIA PROPERTIES ON RESOLVENT OPERATORS

作者：Chang, Yong-Kui^*; Pereira, Aldo; Ponce, Rodrigo

来源：Fractional Calculus and Applied Analysis, 2017, 20(4): 963-987.

DOI：10.1515/fca-2017-0050

• approximate controllability
• Sobolev type differential equations
• fractional derivative
• compact operators

This paper treats the approximate controllability of fractional differential systems of Sobolev type in Banach spaces. We first characterize the properties on the norm continuity and compactness of some resolvent operators (also called solution operators). And then via the obtained properties on resolvent operators and fixed point technique, we give some approximate controllability results for Sobolev type fractional differential systems in the Caputo and Riemann-Liouville fractional derivatives with order 1 < alpha < 2, respectively. Particularly, the existence or compactness of an operator E-1 is not necessarily needed in our results.

• 出版日期2017-8
• 单位西安电子科技大学