Abstract This paper investigates exact voyaging (2 + 1) dimensional Heisenberg ferromagnetic spin chain solutions with conformable fractional derivatives, an important family of nonlinear equations from Schrödinger (NLSE) for the construction of hyperbolic, trigonometric and complex function solutions. The detailed rational sine-cosine system and rational sinh-cosh system were used to locate dim, special and periodic wave solutions successfully. These findings suggest that the proposed approaches may be useful to investigate a range of solutions inside a repository of applied sciences and engineering, with success, quality, and trust. In addition, graphical representations and physical expresses of such solutions are represented by a set of the required values of the parameters involved. The methods are essentially adequate and can be extended to different dynamic models that create the nonlinear processes in today’s research.

RESUMO Um experimento em campo foi conduzido por dois anos consecutivos, a fim de estudar o efeito de diferentes densidades de Parthenium (0, 2, 4, 6, 8, 10, 12, 14 e 16 plantas m-2) sobre os componentes de produção e produtividade de sorgo forrageiro, bem como seu nível de dano econômico. O experimento foi realizado durante o verão, em delineamento de blocos completos (DBC) com quatro repetições. Os resultados mostraram que diferentes densidades de Parthenium reduziram o rendimento e seus componentes do sorgo forrageiro. Contudo, o efeito foi menos proeminente em baixa densidade de Parthenium. Com o aumento da densidade de plantas de Parthenium, observou-se declínio significativo no rendimento e seus componentes Além disso, verificou-se redução na altura das plantas de 17,19% e 15,32%; diâmetro do caule, de 31,79% e 28,10%; número de folhas por planta, de 18,88% e 10,16%; colmo, de 51,01% e 45,03%; e rendimento de forragem fresca, de 24,97% e 26,49%, durante 2013 e 2014, respectivamente. O índice competitivo das plantas de Parthenium, a matéria seca e a captação dos principais nutrientes (NPK) também aumentaram à medida que a densidade delas foi aumentada. O nível de dano econômico sugerido de Parthenium foi de 2,2 plantas m-2, sendo recomendado o seu controle a partir dessa densidade, visando obter alto rendimento e boa qualidade de forragem das plantas de sorgo.

ABSTRACT A field trial was conducted for two consecutive years to evaluate the effect of different parthenium densities (0, 2, 4, 6, 8, 10, 12, 14 and 16 plants m-2) on the yield and yield components of forage sorghum along with parthenium economic threshold level. The experiment was laid out during the summer in a randomized complete block design with four replications. Different parthenium densities reduced yield and yield components of forage sorghum, as the parthenium density increased significant decline in yield and yield components. The highest parthenium density (16 plants m-2) reduced plant height by 17.19% and 15.32%, stem diameter by 31.79% and 28.10%, leaf area per plant by 18.88% and 10.16%, leaf to stem ratio by 51.01% and 45.03% and fresh fodder yield by 24.97% and 26.49% throughout 2013 and 2014, respectively. Parthenium relative competitive index (RCI), dry weight and nutrient uptake (NPK) also increased as parthenium density increased. The suggested economic threshold level of parthenium was 2.2 and 1.6 plants m-2 in 2013 and 2014, respectively. Thus, control the parthenium at this density level is suggested for achieving high yield of good quality sorghum fodder.