TY - JOUR AU - Du, Jun AU - Jiang, Wei AU - Niazi, Azmat Ullah Khan PY - 2017 TI - Approximate controllability of impulsive Hilfer fractional differential inclusions JO - Journal of Nonlinear Sciences and Applications SP - 595--611 VL - 10 IS - 2 AB - In this paper, firstly by utilizing the theory of operators semigroup, probability density functions via impulsive conditions, we establish a new \(PC_{1-\nu}\)-mild solution for impulsive Hilfer fractional differential inclusions. Secondly we prove the existence of mild solutions for the impulsive Hilfer fractional differential inclusions by using fractional calculus, multi-valued analysis and the fixed-point technique. Then under some assumptions, the approximate controllability of associated system are formulated and proved. An example is provided to illustrate the application of the obtained theory SN - ISSN 2008-1901 UR - http://dx.doi.org/10.22436/jnsa.010.02.23 DO - 10.22436/jnsa.010.02.23 ID - Du2017 ER - TY - JOUR TI - Existence and controllability results for nondensely defined impulsive semilinear functional differential inclusions AU - N. Abada AU - M. Benchohra AU - H. Hammouche JO - J. Differential Equations PY - 2009 DA - 2009// VL - 246 ID - Abada2009 ER - TY - JOUR TI - On conformable fractional calculus AU - T. Abdeljawad JO - J. Comput. Appl. Math. PY - 2015 DA - 2015// VL - 279 ID - Abdeljawad 2015 ER - TY - JOUR TI - Existence of fractional neutral functional differential equations AU - R. P. Agarwal AU - Y. Zhou AU - Y.-Y. He JO - Comput. Math. Appl. PY - 2010 DA - 2010// VL - 59 ID - Agarwal2010 ER - TY - BOOK TI - Fractional calculus. Models and numerical methods AU - D. Baleanu AU - K. Diethelm AU - E. Scalas AU - J. J. 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