In this paper, we provide a context for the modeling approaches that have been developed to describe non-Gaussian diffusion behavior, which is ubiquitous in diffusion weighted magnetic resonance imaging of water in biological tissue. Subsequently, we focus on the formalism of the continuous time random walk theory to extract properties of subdiffusion and superdiffusion through novel simplifica...

The main goal of the paper is to use a generalized proportional Riemann–Liouville fractional derivative (GPRLFD) model BAM neural networks and study some stability properties equilibrium. Initially, several GPRLFD are proved, such as squared function. Additionally, comparison results for provided. Two types equilibrium with defined. In connection applied its singularity at initial time, Mittag-...

Linear operators which (1) preserve the reality of zeros of polynomials having only real zeros and (2) map stable polynomials into stable polynomials are investigated using recently established results concerning the zeros of certain Fox–Wright functions and generalized Mittag-Leffler functions. The paper includes several open problems and questions.  2005 Elsevier Inc. All rights reserved.

The main purpose of this paper is to investigate the finite-time stability Hadamard fractional differential equations (HFDEs). Firstly, standard definitions HFDEs in compatible Banach spaces are proposed. In light method successive approximation and Beesack inequality with weakly singular kernel, criteria for linear nonlinear established, respectively. Then regard pure delay, a novel delayed ma...

Abstract: This article focuses on obtaining analytical solutions for d-dimensional, parabolic Volterra integro-differential equations with different types of frictional memory kernel. Based on Laplace transform and Fourier transform theories, the properties of the Fox-H function and convolution theorem, analytical solutions for the equations in the infinite domain are derived under three fricti...