In this paper, we investigate the inverse generator problem for abstract degenerate Volterra integro-differential equations in locally convex spaces. The classes of (a, k)-regularized C-resolvent families and mild $$(C_{1},C_{2})$$ -existence uniqueness play an important role our analysis. We provide several illustrative applications theoretical results obtained primarily to fractional differen...

In this paper, we analyze multi-dimensional quasi-asymptotically $c$-almost periodic functions and their Stepanov generalizations as well Weyl type functions. We also several important subclasses of the class reconsider notion semi-$c$-periodicity in setting, working general framework Lebesgue spaces with variable exponent. provide certain applications our results to abstract Volterra integro-d...

We apply the polynomial least squares method to obtain approximate analytical solutions for a very general class of nonlinear Fredholm and Volterra integro-differential equations. The is relatively simple straightforward one, but its precision this type equations high, fact that illustrated by numerical examples presented. comparison with previous approximations computed included test problems ...

The scope of this study is to establish an effective approximation method for linear first order singularly perturbed Volterra-Fredholm integro-differential equations. finite difference scheme constructed on Shishkin mesh by using appropriate interpolating quadrature rules and exponential basis function. recommended second convergent in the discrete maximum norm. Numerical results illustrating ...

Abstract This paper discusses different types of Ulam stability first-order nonlinear Volterra delay integro-differential equations with impulses. Such allow the presence two kinds memory effects represented by and kernel used fractional integral operator. Our analysis is based on Pachpatte’s inequality fixed point approach Picard operators. Applications are provided to illustrate results obtai...

In this paper, we analyze the Bohr ρ-almost periodic type sequences and generalized of form F:I×X→Y, where ∅≠I⊆Zn, X Y are complex Banach spaces ρ is a general binary relation on Y. We provide many structural results, observations open problems about introduced classes sequences. Certain applications established theoretical results to abstract Volterra integro-difference equations also given.