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 paper, we study a Volterra–Fredholm integro-differential equation. The considered problem involves the fractional Caputo derivatives under some conditions on order. We prove an existence and uniqueness analytic result by application of Banach principle. Then, another that deals with at least one solution is delivered, sufficient for are established means fixed point theorem Schaefer. Ul...

In this article, by using Schaefer fixed point theorem, we establish sufficient conditions for the existence and uniqueness of solutions for a class of impulsive integro-differential equations with nonlocal conditions involving the Caputo fractional derivative.

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.

This paper deals with the exponential stability of a class of nonlinear delay-integrodifferential equations of the form ẋ(t) = f ( t, x(t), x(t − τ1(t)), ∫ t t−τ2(t) g(t, s, x(s))ds ) , t ≥ t0, where τi(t) > 0 for i = 1, 2 and t ≥ t0. The stability relation between ordinary and delay-integro-differential equations is given. It is shown under some suitable conditions that a delay-integro-differe...

A homogeneous fractional-differential equation with a fractional Hardy—Titchmarsh integral and an unbounded operator coefficient in Banach space is considered. The conditions for the representation of solution form Danford—Cauchy are established, exponentially convergent approximation method developed.

although there are many methods for image denoising, but partial differential equation (pde) based denoising attracted much attention in the field of medical image processing such as magnetic resonance imaging (mri). the main advantage of pde-based denoising approach is laid in its ability to smooth image in a nonlinear way, which effectively removes the noise, as well as preserving edge throug...