Analysis of nonlinear Burgers equation with time fractional Atangana-Baleanu-Caputo derivative.

This paper demonstrates, a numerical method to solve the one and two dimensional Burgers' equation involving time fractional Atangana-Baleanu Caputo ( ABC ) derivative with a non-singular kernel. The numerical stratagem consists of a quadrature rule for time fractional ( ABC ) derivative along with Haar wavelet (HW) approximations of one and two dimensional problems. The key feature of the scheme is to reduce fractional problems to the set of linear equations via collocation procedure. Solving the system gives the approximate solution of the given problem. To verify the effectiveness of the developed method five numerical examples are considered. Besides this, the obtained simulations are compared with some published work and identified that proposed technique is better. Moreover, computationally the convergence rate in spatiotemporal directions is presented which shows order two convergence. The stability of the proposed scheme is also described via Lax-Richtmyer criterion. From simulations it is obvious that the scheme is quite useful for the time fractional problems.

Launaea fragilis extract attenuated arthritis in rats through modulation of IL-1ß, TNF-α, IL-6, NF-κB, COX-2, IL-4, and IL-10.

Launaea fragilis (Asso) Pau is a Cholistan desert medicinal plant. Launaea species are used as traditional remedies against various inflammatory conditions. The current research was designed to evaluate the anti-nociceptive, anti-inflammatory, and anti-arthritic potential of ethanolic extract of L. fragilis (Et-LF). The plant extract was prepared by triple maceration. GC-MS screening explored the presence of various bioactive phytoconstituents including n-tetracosanol-1, 1-heptacosanol, and n-hexadecanoic acid. DPPH assay demonstrated the antioxidant potential of Et-LF. Safety profile data indicated that Et-LF was safe up to the oral dose of 5000 mg/kg in female rats. Anti-nociceptive activity of Et-LF was assessed in hot plate method and acetic acid-induced writhing model and the results suggested that Et-LF had significant analgesic effects in both animal models. Carrageenan, histamine, and serotonin-induced edema models were used to estimate the anti-inflammatory effects of Et-LF and were found to prevent paw edema development dose dependently. The anti-arthritic effect of Et-LF was estimated in CFA-induced arthritic rat model. Treatment with Et-LF 125, 250, 500 and flurbiprofen (FP) 10 mg/kg/day significantly attenuated the paw edema, reversed the reduced body weight, and restored the altered hematological parameters in arthritic rats. Gene expression studies revealed the significant downregulation of IL-1ß, TNF-α, IL-6, NF­κB, and COX-2, and upregulation of IL-4 and IL-10 in arthritic rats treated with various doses of plant extract. Histological evaluation of ankle joints showed that Et-LF mitigated pannus formation, infiltration of inflammatory cells, and fibrous connective tissue formation in the diseased rats. Thereof, it may be concluded that the recent study demonstrated the anti-nociceptive, anti-inflammatory, and anti-arthritic effects ascribed to the signifying presence of phytoconstituents in L. fragilis.

Dynamics of the time-fractional reaction-diffusion coupled equations in biological and chemical processes.

This paper aims to demonstrate a numerical strategy via finite difference formulations for time fractional reaction-diffusion models which are ubiquitous in chemical and biological phenomena. The time-fractional derivative is considered in the Caputo sense for both linear and nonlinear problems. First, the Caputo derivative is replaced with a quadrature formula, then an implicit method is used for the remaining part. In the linear case, the proposed strategy reduces the time fractional models into linear simultaneous equations. In nonlinear cases, Quasilinearization is utilized to tackle the nonlinear parts. With this strategy, solutions of the fractional system transform into linear algebraic systems which are easy to solve. Next, the Von Neumann method is implemented to examine the stability of the scheme which discloses that the scheme is unconditionally stable. Further, the applicability of the presented scheme is tested with different linear and nonlinear models which include the one dimensional Schnakenberg and Gray-Scott models, and one and two dimensional Brusselator models. To analyze the accuracy of the present technique two norms namely, L ∞ and L 2 , and relative error are addressed. Moreover, the obtained outcomes are shown tabulated and graphically which identifies that the scheme properly works for the time fractional reaction-diffusion systems.