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Biochar, a carbon-rich solid material and legumes having numerous benefits to the soil-plant system gaining a keen interest as an innovative sustainable approach among the agriculture research community in many parts of the world especially in developing countries in order to enhance soil quality and ensure food security. Thus, with the same approach, we have carried out a field experiment to examine the residual effect of biochar application and summer legumes on soil physical properties and subsequent wheat crop growth at the Research Farm, The University of Agriculture Peshawar during winter 2016-2017. An experiment was designed in two-factor factorial randomized complete block design with three replications in summer 2016 in which three different summer legumes i.e. mungbean, sesbania, and cowpea were grown in the summer for the purpose of grain, green manuring and fodder, a fallow was also included with the purpose of control. Biochar was applied at the rate of 0, 5 and 10 tons ha-1. After the harvesting of summer legumes, sesbania biomass was completely incorporated into the soil while the biomass of other two legumes were removed. The experiment on subsequent wheat was on the same field layout of summer legumes. Both the treatments i.e. previously applied biochar especially 10 tons ha-1 and preceding summer legumes especially sesbania as well as their interaction showed a significant effect on the selected soil physical properties. Similarly, the response of wheat growth was also significant to both treatments but their interaction was non-significant. Thus, it was concluded that both the treatments had a significant effect on the soil physical properties and growth of wheat and should be included in the cropping system.

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In this paper, a comparative study of natural transform decomposition method and new iterative method is presented. The proposed methods are tested upon nonlinear fractional order foam drainage problem and fractional order modified regularized long-wave equation. The solutions obtained by the proposed methods have been compared with the classical solutions and the solution obtained by Adomian decomposition method. Furthermore, the efficiency and reliability of the proposed methods are shown with the help of numerical and graphical results. The fractional order derivatives are defined in Caputo’s sense whose order belongs to the closed interval [0,1]. The results reveal that the methods are quickly convergent and yield encouraging results.

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