Abstract. In this study we developed and modified Taylor expansion method for approximating the solution of linear Fredholm and Volterra integro-differential equations. Via Taylor’s expansion of the unknown function at an arbitrary point, the integro-differential equations to be solved is approximately transformed into a system of linear equations for the unknown and its derivatives which can b...

Deviations from kinetic equilibrium of massive particles caused by the universe expansion are calculated analytically in the Boltzmann approximation. For the case of an energy independent amplitude of elastic scattering, an exact partial differential equation is derived instead of the usual integro-differential one. A simple perturbative solution of the former is found. For the case of an energ...

A new integro-differential equation for diffuse photon density waves (DPDW) is derived within the diffusion approximation. The new equation applies to inhomogeneous bounded turbid media. Interestingly, it does not contain any terms involving gradients of the light diffusion coefficient. The integro-differential equation for diffusive waves is used to develop a 3D-slice imaging algorithm based t...

In this work, a large class of integro-differential equations, arising from the description heat transfer problems, is considered, particularly nonlinear equations. We propose procedure for constructing their solution in very simple and reliable way which only needed tool same one employed to solve linear second-order ordinary differential equation, subject Robin boundary conditions. Proofs con...

We derive heuristically an integro-differential equation, as well as a shell model, governing the dynamics of the Lowest Landau Level equation in a high frequency regime.

In this paper, we study the existence of solution to integro-differential equations in space Lebesgue-integrable on un-bounded interval after transformed nonlinear integral functional equation, used tool is fixed point theorem due Schauder with weak measure non compactness, De-Blasi. addition, give an example which satisfies conditions our theorem.

In this paper, we study a new approach of investigation existence, uniqueness and stability the periodic solution nonlinear fractional integro-differential equation type Caputo-Fabrizio derivative with initial condition, boundary conditions, integral conditions by using successive approximations method Banach fixed point theorem. Finally, some examples are present to illustrate theorems.

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 ...