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...

This paper focuses on the approximate controllability of Hilfer fractional neutral Volterra integro-differential inclusions via almost sectorial operators. Almost operators, differential, Leray-Schauder fixed point theorem and multivalued maps are used to prove result. We start by emphasizing existence a mild solution demonstrate system. In addition, an example is presented principle.

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.

The main goal of this paper is to introduce the condition pseudospectrum multivalued linear operators and prove several relations usual spectrum. We start by giving definition then we focus on characterization, stability some their properties.

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 this paper, we focus on the existence of Hilfer fractional stochastic differential systems via almost sectorial operators. The main results are obtained by using concepts and ideas from calculus, multivalued maps, semigroup theory, operators, fixed-point technique. We start confirming mild solution Dhage’s theorem. Finally, an example is provided to demonstrate considered Hilferr theory.