In this study, a Taylor method is developed for numerically solving the high-order most general nonlinear Fredholm integro-differential-difference equations in terms of Taylor expansions. The method is based on transferring the equation and conditions into the matrix equations which leads to solve a system of nonlinear algebraic equations with the unknown Taylor coefficients. Also, we test the ...

We prove a number of homeomorphism results for nonlinear Fredholm maps of index zero and their perturbations. Moreover, we show that k-ball and k-set perturbations of these homeomorphisms are again homeomorphisms or that the corresponding equations are finitely solvable. Various generalized first Fredholm theorems are given and finite solvability of general ( odd ) Fredholm maps is also studied...

In this article, we solve the second type of nonlinear Volterra picture fuzzy integral equation (NVPFIE) using an accelerated form Adomian decomposition method (ADM). Based on (α,δ,β)-cut, convert NVPFIE to equations in a crisp form. An version ADM is used transformed system, which based new formula for polynomial. The sufficient condition that guarantees unique solution obtained polynomial, er...

In this paper, a new collocation method, which is based on Boubaker polynomials, is introduced for the approximate solutions of a class of two-dimensional linear Fredholm integral equationsof the second kind. The properties of two-dimensional Boubaker functions are presented. The fundamental matrices of integration with the collocation points are utilized to reduce the solution of the integral ...

This manuscript contains several fixed point results for αΓ-F-fuzzy contractive mappings in the framework of orthogonal fuzzy metric spaces. The symmetric property guarantees that distance function is consistent and does not favour any one direction No matter how points are arranged, it enables a fair assessment separations between all them. In results, symmetry condition preserved types self-m...

in this paper we apply the technique of measures of noncompactness to the theory of infinite system of integral equations in the fr´echet spaces. our aim is to provide a few generalization of tychonoff fixed point theorem and prove the existence of solutions for infinite systems of nonlinear integral equations with help of the technique of measures of noncompactness and a generalization of tych...