In the modeling of dynamical problems the fractional order integro-differential equations (IDEs) are very common in science and engineering. The scientists are developing different aspects of these...

https://www.worldscientific.com/doi/pdf/10.1142/S0218348X20400484

Existence results and stability criteria for abc-fuzzy-volterra integro-differential equation

Divide-and-conquer framework for image restoration and enhancement

Existence and uniqueness of an entropy solution for a nonlinear reaction-diffusion system applied to texture analysis

We consider a class of nonlinear parabolic systems driven by Leray-Lions operators with p(x)-growth conditions and strong nonlinearity with respect to the gradients Under the assumption that a nonnegative weak super-solutions is known, we prove the existence of nonnegative weak solutions to the considered systems

Parabolic systems driven by general differential operators with variable exponents and strong nonlinearities with respect to the gradient

The purpose of this work is to study a class of periodic parabolic equations having a critical growth nonlinearity with respect to the gradient and bounded Radon measure. By the main of the sub- and super-solution method, we employ some new technics to prove the existence of a nonnegative weak periodic solution to the studied problems.

Nonnegative weak solution for a periodic parabolic equation with bounded Radon measure

In this paper, we propose a new model of nonlinear and anisotropic reaction diffusion system applied to image restoration and to contrast enhancement. This model is based on a system of partial differential equations of type Fitzhugh-Nagumo. In the first, we give the comparison with the previous model, then, we show the robustness and the performance of our algorithm through a number of experimental results.

Bio-inspired reaction diffusion system applied to image restoration

This work is devoted to the mathematical study of nonlinear and anisotropic reaction-diffusion equation. This type of equation appears in texture synthesis and computer vision. The proposed model utilizesa diffusion tensor which may be adapted to the image structure.

/pdf/texture-synthesis-by-reaction-diffusion-process-2v74cqiw03.pdf

Texture synthesis by reaction diffusion process

As one of the most important tasks in image processing, texture analysis is related to a class of mathematical models that characterize the spatial variations of an image. In this paper, in order to extract features of interest, we propose a reaction diffusion based model which uses the variational approach. In the first place, we describe the mathematical model, then, aiming to simulate the latter accurately, we suggest an efficient numerical scheme. Thereafter, we compare our method to literature findings. Finally, we conclude our analysis by a number of experimental results showing the robustness and the performance of our algorithm.

https://jmm.guilan.ac.ir/article_4611_61d3f592963b388acd8a5af68fabf8f8.pdf

Mariam Zirhem

Papers

Existence and uniqueness of an entropy solution for a nonlinear reaction-diffusion system applied to texture analysis

Bio-inspired reaction diffusion system applied to image restoration

Texture synthesis by reaction diffusion process

A computational model for texture analysis in images with a reaction-diffusion based filter