Mathematical analysis and modeling of fractional order human brain information dynamics including the major effect on sensory memory

In this work, we propose fractional-order deterministic mathematical models for human brain information dynamics, including the major effect on sensory memory. The two models are top-down and bottom-up processing. Mathematical models are analysed for different cases for long and short-term memory effects with the effect of experience and prior knowledge. Studies are conducted both qualitatively and quantitatively to analyse systems using fixed-point theory results. The impact of the global derivative, linear growth, and Lipschitz criteria are used to check the existence and uniqueness of the model for the biological feasibility of the system. Positivity and boundedness of the unique solution were also treated. The global stability of the proposed model is constructed by constructing the first and second derivatives for the Lyapunov function using wave analysis according to the equilibrium point. Numerical simulations of the proposed method in the range of fractional orders are conducted to demonstrate the implications of fractional and fractal orders. To further explore the impact of various parameters on the information processing process in the human brain, information in long-term memory, repetition, and rehearsal Chaotic modelling of the brain information dynamics model is also derived for different cases that are stable and bound to feasible regions. Results demonstrate the strong memory effect by using nonlocal and non-singular kernels at different fractional order values and fractal dimensions, which support experimental and theoretical observations.</p

Conjugates of Degraded and Oxidized Hydroxyethyl Starch and Sulfonylureas: Synthesis, Characterization, and in Vivo Antidiabetic Activity

Orally administered drugs usually face the problem of low water solubility, low permeability, and less retention in bloodstream leading to unsatisfactory pharmacokinetic profile of drugs. Polymer conjugation has attracted increasing interest in the pharmaceutical industry for delivering such low molecular weight (<i>M</i>_w) drugs as well as some complex compounds. In the present work, degraded and oxidized hydroxyethyl starch (HES), a highly biocompatible semisynthetic biopolymer, was used as a drug carrier to overcome the solubility and permeability problems. The HES was coupled with synthesized <i>N</i>-arylsulfonylbenzimidazolones, a class of sulfonylurea derivatives, by creating an amide linkage between the two species. The coupled products were characterized using GPC, FT-IR, ¹H NMR, and ¹³C NMR spectroscopy. The experiments established the viability of covalent coupling between the biopolymer and <i>N</i>-arylsulfonylbenzimidazolones. The coupled products were screened for their in vivo antidiabetic potential on male albino rats. The coupling of sulfonylurea derivatives with HES resulted in a marked increase of the hypoglycemic activity of all the compounds. 2,3-Dihydro-3-(4-nitrobenzensulfonyl)-2-oxo-1<i>H</i>-benzimidazole coupled to HES₁₀₁₀₀ was found most potent with a 67% reduction in blood glucose level of the rats as compared to 41% reduction produced by tolbutamide and 38% by metformin

Dendritic cells <i>D</i>(<i>t</i>) with dimension 0.2.

The value of D(t) using fractal fractional operator with various fractional values at 0.2 dimension.</p

Cancer cells <i>C</i>(<i>t</i>) with dimension 0.2.

The value of C(t) using fractal fractional operator with various fractional values at 0.2 dimension.</p

Tumor cells <i>T</i>(<i>t</i>) with dimension 0.2.

The value of T(t) using fractal fractional operator with various fractional values at 0.2 dimension.</p

Cytokine <i>IL</i>₂(<i>t</i>) with dimension 0.5.

The value of IL2(t) using fractal fractional operator with various fractional values at 0.5 dimension.</p

Anti-PD-L1 inhibitor <i>Z</i>(<i>t</i>) with dimension 0.5.

The value of Z(t) using fractal fractional operator with various fractional values at 0.5 dimension.</p

Cancer cells <i>C</i>(<i>t</i>) with dimension 0.5.

The value of C(t) using fractal fractional operator with various fractional values at 0.5 dimension.</p

Flow chart.

Mathematical formulations are crucial in understanding the dynamics of disease spread within a community. The aim of this work is to examine that the Lung Cancer detection and treatment by introducing IL2 and anti-PD-L1 inhibitor for low immune individuals. Mathematical model is developed with the created hypothesis to increase immune system by antibody cell’s and Fractal-Fractional operator (FFO) is used to turn the model into a fractional order model. A newly developed system TCDIL2Z is examined both qualitatively and quantitatively in order to determine its stable position. The boundedness, positivity and uniqueness of the developed system are examined to ensure reliable bounded findings, which are essential properties of epidemic models. The global derivative is demonstrated to verify the positivity with linear growth and Lipschitz conditions are employed to identify the rate of effects in each sub-compartment. The system is investigated for global stability using Lyapunov first derivative functions to assess the overall impact of IL2 and anti-PD-L1 inhibitor for low immune individuals. Fractal fractional operator is used to derive reliable solution using Mittag-Leffler kernel. In fractal-fractional operators, fractal represents the dimensions of the spread of the disease and fractional represents the fractional ordered derivative operator. We use combine operators to see real behavior of spread as well as control of lung cancer with different dimensions and continuous monitoring. Simulations are conducted to observe the symptomatic and asymptomatic effects of Lung Cancer disease to verify the relationship of IL2, anti-PD-L1 inhibitor and immune system. Also identify the real situation of the control for lung cancer disease after detection and treatment by introducing IL2 cytokine and anti-PD-L1 inhibitor which helps to generate anti-cancer cells of the patients. Such type of investigation will be useful to investigate the spread of disease as well as helpful in developing control strategies from our justified outcomes.</div

Anti-PD-L1 inhibitor <i>Z</i>(<i>t</i>) with dimension 0.2.

The value of Z(t) using fractal fractional operator with various fractional values at 0.2 dimension.</p