in this article,we present a wavelet method for solving stochastic volterra integral equations based on haar wavelets. first, we approximate all functions involved in the problem by haar wavelets then, by substituting the obtained approximations in the problem, using the it^{o} integral formula and collocation points then, the main problem changes into a system of linear or nonlinear equation w...

The current article discusses the existence of monotonic discontinuous solutions for general nonlinear quadratic Volterra-Urysohn functional-integral equations in Orlicz spaces E? when function ? satisfies ?2-condition. case Lebesgue Lp (p > 1) are also examined. We use arguments measure noncompactness with Darbo fixed point theorem to prove our results.

in this paper it is shown that the use of‎ ‎uniform meshes leads to optimal convergence rates provided that‎ ‎the analytical solutions of a particular class of‎ ‎fredholm-volterra integral equations (fvies) are smooth‎.

In this paper we present fuzzy coupled fixed point results in the turf of complete b-metric spaces via nonlinear F-contraction; follow derive some interesting as byproducts. Eventually, apply our solving Volterra integral equations and Caputo-Hadamard type fractional differential equations.