Fibonacci and k Lucas Sequences as Series of Fractions.

In this paper, we defined new relationship between k Fibonacci and k Lucas sequences using continued fractions and series of fractions, this approach is different and never tried in k Fibonacci sequence literature

Existence of solutions for nonlinear mixed type integrodifferential equation of second order

In this paper, we investigate the existence of solutions for nonlinear mixed Volterra-Fredholm integrodifferential equation of second order with nonlocal conditions in Banach spaces. Our analysis is based on Leray-Schauder alternative, rely on a priori bounds of solutions and the inequality established by B. G. Pachpatte

On an abstract nonlinear second order integrodifferential equation

The aim of the present paper is to study the global existence of solutions of nonlinear second order integrodifferential equation in Banach space. Our analysis is based on an application of the Leray-Schauder alternative and rely on a priori bounds of solutions

On Existence of Solutions of Impulsive Nonlinear Functional Neutral Integro-Differential Equations With Nonlocal Condition

In the present paper, we investigate the existence, uniqueness and continuous dependence of mild solutions of an impulsive neutral integro-differential equations with nonlocal condition in Banach spaces. We use Banach contraction principle and the theory of fractional power of operators to obtain our results

On Some Qualitative Properties of Mild Solutions of Nonlocal Semilinear Functional Differential Equations

In the present paper, we investigate the qualitative properties such as existence, uniqueness and continuous dependence on initial data of mild solutions of first and second order nonlocal semilinear functional differential equations with delay in Banach spaces. Our analysis is based on semigroup theory and modified version of Banach contraction theorem

Sobolev-type Volterra-Fredholm functional integrodifferential equations in Banach spaces

This paper deals with the problems such as the existence, uniqueness, continuous dependence and boundedness of mild solution of Volterra-Fredholm functional integrodifferential equations of sobolev type in Banach spaces. Our analysis is based on Banach fixed point principle, the integral inequality established by B. G. Pachpatte, Gronwall-Bellman inequality and the semigroup theory