in this article, we survey the asymptotic stability analysis of fractional differential systems with the prabhakar fractional derivatives. we present the stability regions for these types of fractional differential systems. a brief comparison with the stability aspects of fractional differential systems in the sense of riemann-liouville fractional derivatives is also given.

Drosophila carrying the X-linked mutation dunce (dnc) showed poor learning in a negative reinforcement olfactory conditioning paradigm (Dudai, Y., Y.-N. Jan, D. Byers, W.G. Quinn, and S. Benzer (1976) Proc. Natl. Acad. Sci. U.S.A. 73: 1684-1688). More recently, dnc flies were shown to have reduced activity for one of two cAMP phosphodiesterases (PDEs) present in normal flies, PDE II, whereas PD...

in this paper, boundary value problems of fractional order are converted into an optimal control problems. then an approximate solution is constructed from translations and dilations of a b-spline function such that the exact boundary conditions are satisfied. the fractional differential operators are taken in the riemann-liouville and caputo sense. several example are given and the optimal err...

the classical etiology of erectile dysfunction (ed) comprises aging and vascular, neurogenic, psychological and hormonal components. recent studies have shown that ed can be the forerunner of serious cardiovascular disturbances. it has also been reported that peripheral neuropathy and microvascular injuries caused by pathophysiological changes in patients with diabetes and obesity lead to ed in...

iii 1 Background and Significance 1 2 Preliminary Studies 3 2.1 PDE Time Integrators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.2 PDE Nonlinear Solvers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.3 PDE-constrained Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.4 Linear Solvers . . . ...

Differential evolution (DE) algorithm puts emphasis particularly on imitating the microscopic behavior of individuals, while estimation of distribution algorithm (EDA) tries to estimate the probabilistic distribution of the entire population. DE and EDA can be extended to multi-objective optimization problems by using a Pareto-based approach, called Pareto DE (PDE) and Pareto EDA (PEDA) respect...

In the inherited retinal degeneration of rd mice, cyclic GMP accumulates in affected rod photoreceptors prior to their degeneration. A deficiency in the activity of the visual cell phosphodiesterase apparently results in the accumulation of cyclic GMP. The cyclic GMP phosphodiesterase (PDE) of normal mouse photoreceptors is a heteromeric protein complex of about 170 kDa, consisting of the alpha...

We study Mean Field Games (MFGs) driven by a large class of nonlocal, fractional and anomalous diffusions in the whole space. These non-Gaussian are pure jump Lévy processes with some ?-stable like behaviour. Included Laplace diffusion operators (??)?2, tempered nonsymmetric Finance, spectrally one-sided processes, sums subelliptic different orders. Our main results existence uniqueness classic...

BNG-1, a novel mixture of traditional Chinese medicines with a long history in the treatment of stroke, exhibited acute neuroprotection effect on rats with middle cerebral artery occlusion (MCAO). Anti-ischemic effects were seen in both animals receiving BNG-1 before the ischemic insult as well as in animals receiving the drug formulation after surgical occlusion of the artery. Anti-thrombic ac...

The cyclic nucleotides, cyclic adenosine monophosphate (cAMP) and cyclic guanosine monophosphate (cGMP) play an important role in the regulation of airway smooth muscle tone and activation of inflammatory cells. Intracellular concentrations of these nucleotides are tightly regulated by phosphodiesterases (PDEs). Several families of PDEs are now recognized and, within each isoenzyme family, mole...