New discussion on nonlocal controllability for fractional evolution system of order $1 < r < 2$

In this manuscript, we deal with the nonlocal controllability results for the fractional evolution system of $1< r<2$ 1 < r < 2 in a Banach space. The main results of this article are tested by using fractional calculations, the measure of noncompactness, cosine families, Mainardi’s Wright-type function, and fixed point techniques. First, we investigate the controllability results of a mild solution for the fractional evolution system with nonlocal conditions using the Mönch fixed point theorem. Furthermore, we develop the nonlocal controllability results for fractional integrodifferential evolution system by applying the Banach fixed point theorem. Finally, an application is presented for drawing the theory of the main results.

Results on the approximate controllability of fractional hemivariational inequalities of order $1< r<2$

In this paper, we investigate the approximate controllability of fractional evolution inclusions with hemivariational inequalities of order $1< r<2$ 1 < r < 2 . The main results of this paper are verified by using the fractional theories, multivalued analysis, cosine families, and fixed-point approach. At first, we discuss the existence of the mild solution for the class of fractional systems. After that, we establish the approximate controllability of linear and semilinear control systems. Finally, an application is presented to illustrate our theoretical results.

A note on C0-groups and C-groups on non-archimedean Banach spaces

In this paper, we introduce new classes of linear operators so called [Formula: see text]-groups, [Formula: see text]-groups and cosine families of bounded linear operators on non-archimedean Banach spaces over non-archimedean complete valued field [Formula: see text]. We show some results about it.