An iterative solution of the quadratic equation in Banach space

An Iterative Solution of the Quadratic Equation in Banach Space

I. Introduction. The solutions of the quadratic equation ax2 + bx+c = 0, where a, b, and c are real numbers, are given in exact form by the quadratic formula. Moreover, if the roots are real and irrational, Newton's method or continued fractions may be used to approximate the solutions.

Positive Solution of Singular Fractional Differential Equation in Banach Space

Recently, fractional differential equations have been investigated extensively. The motivation for those works rises from both the development of the theory of fractional calculus itself and the applications of such constructions in various sciences such as physics, chemistry, aerodynamics, and electrodynamics of the complex medium. For examples and details, see 1–5 and the references therein. ...

Quadratic Integral Equations in Reflexive Banach Space

This paper is devoted to proving the existence of weak solutions to some quadratic integral equations of fractional type in a reflexive Banach space relative to the weak topology. A special case will be considered.

Numerical Solution of Sawada-Kotera equation by using Iterative Methods

The existence result of a fuzzy implicit integro-differential equation in semilinear Banach space

In this paper‎, ‎the existence and uniqueness of the ‎solution of a nonlinear fully fuzzy implicit integro-differential equation‎ ‎arising in the field of fluid mechanics is investigated. ‎First,‎ an equivalency lemma ‎is ‎presented ‎by‎ which the problem understudy ‎is ‎converted‎ to ‎the‎ two different forms of integral equation depending on the kind of differentiability of the solution. Then...