In this paper, we apply the local fractional Laplace transform method (or Yang-Laplace transform) on Volterra integro-differential equations of the second kind within the local fractional integral operators to obtain the analytical approximate solutions. The iteration procedure is based on local fractional derivative operators. This approach provides us with a convenient way to find a solution ...

1 Product measures Let (X,A , μ) be a σ-finite measure space. Then with A ⊗ A the product σalgebra and μ ⊗ μ the product measure on A ⊗A , (X ×X,A ⊗A , μ⊗ μ) is itself a σ-finite measure space. Write Fx(y) = F (x, y) and F (x) = F (x, y). For any measurable space (X ′,A ′), it is a fact that if F : X×X → X ′ is measurable then Fx is measurable for each x ∈ X and F y is measurable for each y ∈ X...

in the present paper, we prove subordination, superordination and sandwich-type properties of a certain integral operators for univalent functions on open unit disc, moreover the special behavior of this class is investigated.

let $c_0(alpha)$ denote the class of concave univalent functions defined in the open unit disk $mathbb{d}$. each function $f in c_{0}(alpha)$ maps the unit disk $mathbb{d}$ onto the complement of an unbounded convex set. in this paper, we study the mapping properties of this class under integral operators.

Darbo's fixed point theorem and its generalizations play a crucial role in the existence of solutions in integral equations. Meir-Keeler condensing operators is a generalization of Darbo's fixed point theorem and most of other generalizations are a special case of this result. In recent years, some authors applied these generalizations to solve several special integral equations and some of the...

In this article we decide to define a modified homotopy perturbation for solving non-linear integral equations. Almost, all of the papers that was presented to solve non-linear problems by the homotopy method, they used from two non-linear and linear operators. But we convert a non-linear problem to two suitable non-linear operators also we use from appropriate bases functions such as Legendre ...

In the present article we discuss approximation properties of genuine Lupac{s}-Beta operators of  integral type. We establish quantitative asymptotic formulae and a direct estimate in terms of Ditzian-Totik modulus of continuity. Finally we mention  results on the weighted modulus of continuity for the genuine operators.

In this paper, we apply the local fractional Adomian decomposition and variational iteration methods to obtain the analytic approximate solutions of Fredholm integral equations of the second kind within local fractional derivative operators. The iteration procedure is based on local fractional derivative. The obtained results reveal that the proposed methods are very efficient and simple tools ...

In this article to prove existence of solution of infinite system of nonlinear integral equations, we consider the space of solution containing all convergence sequences with a finite limit, as with a suitable norm is a Banach space. By creating a generalization of Meir-Keeler condensing operators which is named as F-generalized Meir-Keeler condensing operators and measure of noncompactness, we...