In this paper, the continuse Legendre wavelets constructed on the interval [0, 1] are used to solve the Nonlinear Fredholm integro-differential equation. The Nonlinear part of integro-differential is ap- proximated by Legendre wavelets, and the Nonlinear integro-differential is reduced to a system of Nonlinear equations. We give some numerical examples to show applicability of the proposed method.

In this paper, we prove the generalized Hyers-Ulam-Rassias stability of a Nonlinear additive functional equation in RNS.

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This paper is devoted to prove the existence of extremal solutions for multi-term Nonlinear fractional differential equations with Nonlinear boundary conditions. The fractional derivative is of Caputo type and the inhomogeneous term depends on the fractional derivatives of lower orders. By establishing a new comparison theorem and applying the monotone iterative technique, we show the existence of extremal solutions. The method is a constructive method that yields monotone sequences that converge to the extremal solutions. As an application, some examples are presented to illustrate the main results.

In this paper, we first introduce the concepts of an equilibrium region and a stable equilibrium region. Then, we state and prove conditions under which a Nonlinear autonomous system has a stable equilibrium region. It will be shown that these concepts and stability conditions are generalizations of the corresponding concepts of equilibrium points and asymptotical stable equilibrium points and their stability conditions. Using these conditions and Poincare-Bendixson theorem, we discuss conditions for the existence of periodic solutions in a Nonlinear system of ordinary differential equations.