Existence results for nonlinear quadratic integral equations of fractional order in Banach algebra

Abstract

We present an existence theorem for at least one continuous solution for a nonlinear quadratic functional integral equation of fractional order. Also, a general quadratic integral of fractional order will be considered.MSC 2010 : Primary 26A33; Secondary 45D05, 60G22, 33E30

Fixed point theorems in Fréchet algebras and Fréchet spaces and applications to nonlinear integral equations

“…A lot of these equations were considered in Banach algebra (cf. [1,5,6,9,10,14,15]) but only few were investigated in Fréchet algebra [8]. However, it seems that convenient environment for integral equations on unbounded interval R + are various Fréchet function spaces, which in the case of some types of the product integral equations, naturally lead to Fréchet algebras.…”

Monotone Solution of Cauchy Type Weighted Nonlocal Fractional Differential Equation

“…We will use extensively studied fractional derivative and integral with its properties by [6,7,10,11,16,17,18,19,20,23,24,25] Let E denote a partially ordered real normed linear space with an order relation ≼ and the norm ∥ · ∥. It is known that E is regular if {x n } n∈N is a non-decreasing (resp.…”

On the Weak Solutions of a Delay Composite Functional Integral Equation of Volterra-Stieltjes Type in Reflexive Banach Space

“…The existence of weak solutions for ordinary differential equations in Banach spaces has been investigated in many papers, for example, in Cicho ń [1,2], Cramer et al [3], Knight [4], Kubiaczyk and Szufla [5], and [6][7][8][9][10][11] and the references therein for fractionalorder differential equations in Banach spaces, and [12][13][14] for quadratic integral equations in reflexive Banach algebra.…”