Search

In this paper, by using the Caputo-Katugampola fractional derivative concept for the interval functions, a non-instantaneous impulsive value problem of interval differential equations is investigated. The first purpose is to study the existence and uniqueness results of the solution of the given problem, and the second purpose is to present the Ulam-Hyers-Mittag-Leffler's stability results of the above problem. Finally, some examples are given to illustrate our main results.

Due to the complexly natural attributes of technical systems, reality has been shown that many systems could be modeled more precisely if they are modeled by using fractional calculus and fractional-order differential equations. Inspired by this advantage, in this work a fractional-order derivative-based sliding mode controller (FD-SMC) for magneto-rheological damper based on semi-active vehicle suspensions (MRD-SAVSs) is proposed to make the states of the given system asymptotically stable in the finite time. To show this assertion, a new estimate result for fractional differential inequality is presented to derive an FD-SMC law for the systems of MRD-SAVS. Then, this corresponding fractional-order sliding mode controller is designed to provide robustness, high performance control, finite time convergence in the presence of uncertainties and external disturbances. Finally, numerical simulation results are presented to demonstrate the effectiveness of the proposed control method.

The inhibition of glutaminyl cyclase (QC) may provide a promising strategy for the treatment of early Alzheimer's disease (AD) by reducing the amount of the toxic pyroform of β-amyloid (AβΝ3pE) in the brains of AD patients. In this work, we identified potent QC inhibitors with subnanomolar IC50 values that were up to 290-fold higher than that of PQ912, which is currently being tested in Phase II clinical trials. Among the tested compounds, the cyclopentylmethyl derivative (214) exhibited the most potent in vitro activity (IC50 = 0.1 nM), while benzimidazole (227) showed the most promising in vivo efficacy, selectivity and druggable profile. 227 significantly reduced the concentration of pyroform Aβ and total Aβ in the brain of an AD animal model and improved the alternation behavior of mice during Y-maze tests. The crystal structure of human QC (hQC) in complex with 214 indicated tight binding at the active site, supporting that the specific inhibition of QC results in potent in vitro and in vivo activity. Considering the recent clinical success of donanemab, which targets AβΝ3pE, small molecule-based QC inhibitors may also provide potential therapeutic options for early-stage AD treatment.

This paper is devoted to considering the existence and uniqueness results for fuzzy fractional functional integral equations employing the contraction principle. Moreover, the approach is followed to prove the existence and uniqueness of solutions for the fuzzy fractional functional initial value problem under Caputo-type fuzzy fractional derivatives. Finally, the solution to fuzzy fractional functional initial value problem under Caputo-type fuzzy fractional derivatives by a modified fractional Euler method (MFEM) is presented. The method is illustrated by solving some examples.

Pyroglutamate-modified amyloid β peptides (pGlu-Aβ) are highly neurotoxic and promote the formation of amyloid plaques. The pGlu-Aβ peptides are generated by glutaminyl cyclase (QC), and recent clinical studies indicate that QC represents an alternative therapeutic target to treat Alzheimer’s disease (AD). We have previously developed a series of QC inhibitors with an extended pharmacophoric scaffold, termed the Arg-mimetic D-region. In the present study, we focused on the structure activity relationship (SAR) of analogues with modifications in the D-region and evaluated their biological activity. Most compounds in this series exhibited potent activity in vitro, and our SAR analysis and the molecular docking studies identified compound 202 as a potential candidate because it forms an additional hydrophobic interaction in the h QC active site. Overall, our study provides valuable insights into the Arg-mimetic pharmacophore that will guide the design of novel QC inhibitors as potential treatments for AD.

A series of α-substituted acetamide derivatives of previously reported 2-(3-fluoro-4-methylsulfonamidophenyl)propanamide leads (1, 2) were investigated for antagonism of hTRPV1 activation by capsaicin. Compound 34, which possesses an α-m-tolyl substituent, showed highly potent and selective antagonism of capsaicin with Ki(CAP) = 0.1 nM. It thus reflected a 3-fold improvement in potency over parent 1. Docking analysis using our homology model indicated that the high potency of 34 might be attributed to a specific hydrophobic interaction of the m-tolyl group with the receptor.

Glutaminyl cyclase (QC) has been implicated in the formation of toxic amyloid plaques by generating the N-terminal pyroglutamate of β-amyloid peptides (pGlu-Aβ) and thus may participate in the pathogenesis of Alzheimer’s disease (AD). We designed a library of glutamyl cyclase (QC) inhibitors based on the proposed binding mode of the preferred substrate, Aβ3E−42. An in vitro structure–activity relationship study identified several excellent QC inhibitors demonstrating 5- to 40-fold increases in potency compared to a known QC inhibitor. When tested in mouse models of AD, compound 212 significantly reduced the brain concentrations of pyroform Aβ and total Aβ and restored cognitive functions. This potent Aβ-lowering effect was achieved by incorporating an additional binding region into our previously established pharmacophoric model, resulting in strong interactions with the carboxylate group of Glu327 in the QC binding site. Our study offers useful insights in designing novel QC inhibitors as a potential tre...

In this paper, a class of new stochastic differential equations on semilinear Hausdorff space under Hukuhara derivative, called set-valued stochastic differential equations (SSDEs) driven by a Wiener process. Moreover, some corresponding properties of SSDEs are discussed such as existence, uniqueness of solution. Finaly, we give some applications to models of interval-valued stochastic differential equations such as stock prices model and the Langevin equation.

In this study, we consider the interval-valued integro-differential equations (IIDEs) under generalized H-differentiability D H g X ( t ) = F ( t , X ( t ) ) + ∫ t 0 t G ( t , s , X ( s ) ) d s , X ( t 0 ) = X 0 ∈ K C ( R ) . The global existence of solutions for interval-valued integro-differential equations with initial conditions under generalized H-differentiability is studied. Theorems for global existence of solutions are given and proved on [ t 0 , ∞ ) . Some examples are given to illustrate these results. MSC:34K05, 34K30, 47G20.

In this paper, we present a generalized concept of second-order differentiability for interval-valued functions. The global existence of solutions for interval-valued second-order differential equations (ISDEs) under generalized H-differentiability is proved. We present some examples of linear interval-valued second-order differential equations with initial conditions having four different solutions. Finally, we propose a new algorithm based on the analysis of a crisp solution. Some examples are given by using our proposed algorithm. MSC:34K05, 34K30, 47G20.