Fractional derivative

Cell-free DNA (cfDNA) profiling is increasingly used to guide cancer care, yet mutations are not always identified. The ability to detect somatic mutations in plasma depends on both assay sensitivity and the fraction of circulating DNA in plasma that is tumor-derived (i.e., cfDNA tumor fraction).

15p vibransone 28-03-2024 3 2   Download

In this article, a functional semilinear Rayleigh-Stokes equation involving a fractional derivative with delay is investigated. The paper employs the time-fractional derivative which is Riemann-Liouville type.

8p vimalfoy 08-02-2023 4 3   Download

Here it was investigated how oligonucleotide retention and selectivity factors are affected by electrostatic and non-electrostatic interactions in ion pair chromatography. A framework was derived describing how selectivity depends on the electrostatic potential generated by the ion-pair reagent concentration, co-solvent volume fraction, charge difference between the analytes, and temperature.

12p viginny 23-12-2022 7 3   Download

The purification of extracellular vesicles (EVs) remains a major hurdle in the progression of fundamental research and the commercial application of EV-based products. In this study, we evaluated the potential of heparin affinity chromatography (HAC) to purify neural stem cell-derived EVs as part of a multistep process.

16p viginny 23-12-2022 6 3   Download

This paper is devoted to study a fractional equation involving Caputo-Katugampola derivative with nonlocal initial condition. Unlike previous papers, in this paper, the source function of problem is assumed having a singularity.

9p vispyker 14-11-2022 7 2   Download

In the paper "Remarks on decaying solutions to distributed order differential equations", we present results on the asymptotic behavior of the solutions to distributed order differential equations in Euclidean spaces. The paper develops some recent results in [1] on fractional differential equations to the case of more general nonlocal derivatives. We utilize the detailed behavior of the relaxation functions instead of the Mittag–Leffler functions. The typical decaying rate is logarithmic due to the ultra-slow phenomenon.

7p runordie3 27-06-2022 13 2   Download

In this paper, we consider the problem of fractional exponential stability for a class of Hopfield fractional-order neural networks (FONNs) subject to conformable derivative and convex polytopic uncertainties.

7p viirenerosenfeld 02-06-2022 11 3   Download

The simulation result demonstrated that the Runge–Kutta–Nystrom¨ algorithm using the second order derivative for the vibration analysis of systems involving fractional derivatives is more effective than the Newmark algorithm of Zhang and Shimizu.

12p inception36 30-11-2021 15 1   Download

This control structure is inflexible since using fixed gains. For overcoming this weakness, we integrate variable fractional-order derivative into SMC that leads to an adaptive system with adjustable parameters. We use Mittag–Leffler stability, an enhanced version of Lyapunov theory, to analyze the convergence of closed-loop system. Applying the controller to a practical crane shows the efficiency of proposed control approach. The controller works well and keeps the output responses consistent despite the large variation of crane parameters.

8p spiritedaway36 28-11-2021 12 2   Download

Scutellaria salviifolia Benth. is an endemic species growing in Turkey that belongs to the family Lamiaceae. As a result of a phytochemical study on the aerial parts of S. salviifolia Benth., two new and 10 known compounds were isolated from the aqueous fraction of methanolic extract. The new compounds are methyl-α-pyrone glucosides, 3,4-dihydroxy-6-methylpyran-2-one 3-O-β -glucopyranoside (=scusalvioside A, 1), and 3,4-dihydroxy-6-methylpyran2-one 3-O-β -(6′ -O-E -caffeoyl) glucopyranoside (=scusalvioside B, 2) with new skeletal structures.

10p tudichquannguyet 29-11-2021 12 1   Download

Chromatographic separation of n-hexane and ethyl acetate fraction of a crude methanol extract obtained from aerial parts of the Scorzonera aucheriana DC collected from Sivas province of Turkey yielded nine natural compounds; two new 3-caffeoyl-quinic acid analogs (1-2), one new taraxasterol oleate (3), and six known triterpenoids taraxasterol (4), taraxasterol acetate (5), ptiloepoxide (6), lupeol (7), lupeol acetate (8), and β-sitosterol (9) were characterized.

11p tudichquannguyet 29-11-2021 4 1   Download

The results showed that smaller peptide fractions had higher ACE inhibitory activity. At concentration of 30 µg/mL, inhibitory activitiy of peptides with molecular sizes ≤ 10, 5, 3 kDa was 16.3, 27.7 and 32.7%, respectively, and the best IC50 was 48,85 µg/ml. The lowest peptide concentration for completely inhibition bacteria after 24 h of incubation was 30 mg/mL (V. cholerae), 35 mg/mL (E. coli) and 50 mg/mL (S. typhi).

10p spiritedaway36 25-11-2021 12 1   Download

Lecture Calculus - Chapter 9: Computing derivatives. After studying this section will help you understand: we list and prove the rules first, they are rather easy to prove; let us state all five of them as one theorem, and prove it,...

14p diepchilang 22-08-2021 7 1   Download

In addition, the displacement field of THSDT needs the high continuity in approximated formulation with high-order derivatives for a weak form of fourth order equation. According to IGA formulation based on the generalized THSDT, the shear locking phenomenon is free. The variables of THSDT are less than HSDTs which contain five DOFs per node. The influences of weight fractions, the coefficient porosity, dispersion patterns of GPLs and distribution types of porosity on structure’s natural frequencies are studied through some numerical examples.

16p chauchaungayxua12 09-07-2021 13 2   Download

This paper considersa generalization of fractional Bessel type process. It is also a type of singular stochastic differential equations driven by fractional Brownian motion which were studied by some authors. Undersome assumptions of coefficients, this equation has a unique positive solution.

7p nguaconbaynhay12 13-06-2021 18 1   Download

Chapter 18 - Money demand and money supply. The main contents of this chapter include all of the following: Money demand (and some supply), the price of money, derivations of the pricing relations, money and sticky prices, money in models of monopolistic competition, money and price setting, monetary policy, empirical measures of the effect of money on output.

42p lovebychance02 04-05-2021 14 2   Download

This paper is concerned with the nonlinear dynamic buckling of sandwich functionally graded circular cylinder shells filled with fluid. Governing equations are derived using the classical shell theory and the geometrical nonlinearity in von Karman–Donnell sense is taken into account. Solutions of the problem are established by using Galerkin’s method and Runge–Kutta method. Effects of thermal environment, geometric parameters, volume fraction index k and fluid on dynamic critical loads of shells are investigated.

14p nguaconbaynhay11 07-04-2021 17 1   Download

Adipose-derived stromal vascular fraction (SVF) cells are a mixed cell population that includes cells with multilineage potential, similar to bone marrow-derived mesenchymal stem cells. Our purpose is to investigate the influence of SVF cells in patients with knee osteoarthritis (OA) and the short-term treatment effects.

10p vimariana2711 22-12-2020 9 1   Download

In this paper, we present a result on Hyers-Ulam stability for a class of nonlocal differential equations in Hilbert spaces by using the theory of integral equations with completely positive kernels together with a new Gronwall inequality type. The paper develops some recent results on fractional differential equations to the ones involving general nonlocal derivatives. Instead of Mittag-Leffler functions, we must utilize the characterization of relaxation function.

7p tamynhan5 10-12-2020 11 2   Download

This paper the analysis and use of these conditions. Since the conditions involve norms of functionals in fractional Sobolev spaces, we derive ‘stronger’ conditions that are simpler in form. These new conditions pave the way for the inf-sup testing, a tool for assessing the stability of the discretized problems.

30p trinhthamhodang9 10-12-2020 12 0   Download