in this paper we investigate the existence and uniqueness for volterra-fredholm type integral equations and extension of this type of integral equations. the result is obtained by using the  coupled fixed point theorems in the framework of banach space $ x=c([a,b],mathbb{r})$. finally, we  give an example to illustrate the applications of our results.

in this work, a new iterative method is proposed for obtaining the approximate solution of a class of hammerstein type integral equations system. the main structure of this method is based on the richardson iterative method for solving an algebraic linear system of equations. some conditions for existence and unique solution of this type equations are imposed. convergence analysis and error bou...

A type of nonlinearity in vibrational engineering systems emerges when the restoring force is a nonlinear function of displacement. The derivative of this function is known as stiffness. If the stiffness increases by increasing the value of displacement from the equilibrium position, then the system is known as hardening type oscillator and if the stiffness decreases by increasing the value of ...

the construction of fractional type of flatlet biorthogonal multiwavelet system is investigated in this paper. we apply this system as basis functions to solve the fractional differential and integro-differential equations. biorthogonality and high vanishing moments of this system are two major properties which lead to the good approximation for the solutions of the given problems. some test pr...

in this paper we propose a method for solving some well-known classes of lane-emden type equations which are nonlinear ordinary differential equations on the semi-in nite domain. the proposed approach is based on an unsupervised combined arti cial neural networks (ucann) method. firstly, the trial solutions of the differential equations are written in the form of feed-forward neural networks co...

‎We study dual integral equations which appear in formulation of the‎ ‎potential distribution of an electrified plate with mixed boundary‎ ‎conditions‎. ‎These equations will be converted to a system of‎ ‎singular integral equations with Cauchy type kernels‎. ‎Using‎ ‎Chebyshev polynomials‎, ‎we propose a method to approximate the‎ ‎solution of Cauchy type singular integral equation which will ...

We study Riemann-type functional equations with respect to value-distribution theory and derive implications for their solutions. In particular, a fixed complex number $a\neq0$ function from the Selberg class $\mathcal{L}$, we prove Riemann-von Mangoldt formula of a-points $\Delta$-factor equation $\mathcal{L}$ an analog Landau's over these points. From last that ordinates $a$-points are unifor...