and Applied Analysis 3 concrete situations. Indeed, we consider an example with a particular choice of the function b and the operator A is defined by Aw t, ξ a1 ξ ∂2 ∂ξ2 w t, ξ b1 ξ ∂ ∂ξ w t, ξ c ξ w t, ξ , 1.3 where the given coefficients a1, b1, c satisfy the usual uniform ellipticity conditions. 2. Preliminaries Most of the notations used throughout this paper are standard. So, N, Z, R, and...

A new system of nonlinear fuzzy variational inclusions involving A, η -accretive mappings in uniformly smooth Banach spaces is introduced and studiedmany fuzzy variational and variational inequality inclusion problems as special cases of this system. By using the resolvent operator technique associated with A, η -accretive operator due to Lan et al. and Nadler’s fixed points theorem for set-val...

The paper presents the foundations of theory linear fractional Volterra integro-differential equations convolution type in Banach spaces. It is established that existence a resolvent operator for such equivalent to well-posedness formulation initial problem them. Within framework this approach, theorem Hille–Yosida proved.

where it is assumed that the “resolvent” L, = (T + (l/n)l)-i, II = 1, 2,... exists and is defined at least on the range of the operator f C. Such a class of operators T includes all m-accretive operators (cf. Kato ] 5 I). The equations (G,) can be solved by a degree theory argument if we assume, among other things, that L, is compact and C is continuous and bounded, or that L, is continuous and...

This article investigates the approximate controllability of second order non-autonomous functional evolution equations involving non-instantaneous impulses and nonlocal conditions. First, we discuss linear system in detail, which lacks existing literature. Then, derive sufficient conditions for our separable reflexive Banach spaces via operator, resolvent operator conditions, Schauder’s fixed ...