The Multifunctional Role of Chitosan in Horticultural Crops; A Review.

Chitosan is a naturally occurring compound and is commercially produced from seafood shells. It has been utilized in the induction of the defense system in both pre and post-harvest fruits and vegetables against fungi, bacteria, viruses, and other abiotic stresses. In addition to that, chitosan effectively improves the physiological properties of plants and also enhances the shelf life of post-harvest produces. Moreover, chitosan treatment regulates several genes in plants, particularly the activation of plant defense signaling pathways. That includes the elicitation of phytoalexins and pathogenesis-related (PR) protein. Besides that, chitosan has been employed in soil as a plant nutrient and has shown great efficacy in combination with other industrial fertilizers without affecting the soil's beneficial microbes. Furthermore, it is helpful in reducing the fertilizer losses due to its coating ability, which is important in keeping the environmental pollution under check. Based on exhibiting such excellent properties, there is a striking interest in using chitosan biopolymers in agriculture systems. Therefore, our current review has been centered upon the multiple roles of chitosan in horticultural crops that could be useful in future crop improvement programs.

A survey on fractal fractional nonlinear Kawahara equation theoretical and computational analysis.

With the use of the Caputo, Caputo-Fabrizio (CF), and Atangana-Baleanu-Caputo (ABC) fractal fractional differential operators, this study offers a theoretical and computational approach to solving the Kawahara problem by merging Laplace transform and Adomian decomposition approaches. We show the solution's existence and uniqueness through generalized and advanced version of fixed point theorem. We present a precise and efficient method for solving nonlinear partial differential equations (PDEs), in particular the Kawahara problem. Through careful error analysis and comparison with precise solutions, the suggested method is validated, demonstrating its applicability in solving the nonlinear PDEs. Moreover, the comparative analysis is studied for the considered equation under the aforementioned operators.

Explicit scheme for solving variable-order time-fractional initial boundary value problems.

The creation of an explicit finite difference scheme with the express purpose of resolving initial boundary value issues with linear and semi-linear variable-order temporal fractional properties is presented in this study. The rationale behind the utilization of the Caputo derivative in this scheme stems from its known importance in fractional calculus, an area of study that has attracted significant interest in the mathematical sciences and physics. Because of its special capacity to accurately represent physical memory and inheritance, the Caputo derivative is a relevant and appropriate option for representing the fractional features present in the issues this study attempts to address. Moreover, a detailed Fourier analysis of the explicit finite difference scheme's stability is shown, demonstrating its conditional stability. Finally, certain numerical example solutions are reviewed and MATLAB-based graphic presentations are made.

Dynamics of the optimality control of transmission of infectious disease: a sensitivity analysis.

Over the course of history global population has witnessed deterioration of unprecedented scale caused by infectious transmission. The necessity to mitigate the infectious flow requires the launch of a well-directed and inclusive set of efforts. Motivated by the urge for continuous improvement in existing schemes, this article aims at the encapsulation of the dynamics of the spread of infectious diseases. The objectives are served by the launch of the infectious disease model. Moreover, an optimal control strategy is introduced to ensure the incorporation of the most feasible health interventions to reduce the number of infected individuals. The outcomes of the research are facilitated by stratifying the population into five compartments that are susceptible class, acute infected class, chronic infected class, recovered class, and vaccinated class. The optimal control strategy is formulated by incorporating specific control variables namely, awareness about medication, isolation, ventilation, vaccination rates, and quarantine level. The developed model is validated by proving the pivotal delicacies such as positivity, invariant region, reproduction number, stability, and sensitivity analysis. The legitimacy of the proposed model is delineated through the detailed sensitivity analysis along with the documentation of local and global features in a comprehensive manner. The maximum sensitivity index parameters are disease transmission and people moved from acute stages into chronic stages whose value is (0.439, 1) increase in parameter by 10 percent would increase the threshold quantity by (4.39, 1). Under the condition of a stable system, we witnessed an inverse relationship between susceptible class and time. Moreover, to assist the gain of the fundamental aim of this research, we take the control variables as time-dependent and obtain the optimal control strategy to minimize infected populations and to maximize the recovered population, simultaneously. The objectives are attained by the employment of the Pontryagin maximum principle. Furthermore, the efficacy of the usual health interventions such as quarantine, face mask usage, and hand sanitation are also noticed. The effectiveness of the suggested control plan is explained by using numerical evaluation. The advantages of the new strategy are highlighted in the article.

Analysis of SIQR type mathematical model under Atangana-Baleanu fractional differential operator.

In the given manuscript, the fractional mathematical model for the current pandemic of COVID-19 is investigated. The model is composed of four agents of susceptible (S), infectious (I), quarantined (Q) and recovered (R) cases respectively. The fractional operator of Atangana-Baleanu-Caputo (ABC) is applied to the considered model for the fractional dynamics. The basic reproduction number is computed for the stability analysis. The techniques of existence and uniqueness of the solution are established with the help of fixed point theory. The concept of stability is also derived using the Ulam-Hyers stability technique. With the help of the fractional order numerical method of Adams-Bashforth, we find the approximate solution of the said model. The obtained scheme is simulated on different fractional orders along with the comparison of integer orders. Varying the numerical values for the contact rate ζ, different simulations are performed to check the effect of it on the dynamics of COVID-19.