Existence results for Caputo fractional mixed Volterra-Fredholm-type integrodifferential inclusions of order r ∈ (1, 2) with sectorial operators

Abstract

Fractional differential equations are used in many areas, such as the fields of science. In this paper, we study existence results for a class of fractional mixed Volterra-Fredholm-type integrodifferential inclusions of order 1 <r < 2 with the sectorial operator in Banach space. Firstly, a more appropriate concept for mild solutions is introduced. Secondly, the existence of mild solution is investigated by using the fractional calculus, multivalued map, and fixed point theorem with the sectorial operator of type (P,η,r,γ). Further, the result is extended to obtain the conditions for the existence of fractional mixed Volterra-Fredholm-type integrodifferential inclusions with nonlocal conditions. Finally, an application is developed to illustrate the theory of the obtained result.