In the current paper, we carry out an investigation into the exact solutions of the (3+1)-dimensional space-time fractional modified KdV–Zakharov–Kuznetsov (fractional mKdV–ZK) equation. Based on the conformable fractional derivative and its properties, the fractional mKdV–ZK equation is reduced into an ordinary differential equation which has been solved analytically by the variable separated ODE method. Various types of analytic solutions in terms of hyperbolic functions, trigonometric functions and Jacobi elliptic functions are derived. All conditions for the validity of all obtained solutions are given.
A.Z. Khan, T. Shah, S. Khan, A. Rehman, H. Akbar, A. Muhammad and S.K. Khalil
The objective of this study was to assess the comparative efficiency of different priming techniques on germination and early seedling growth of maize cultivars. Laboratory experiments were conducted to examine the efficacy of different seed invigoration treatments on seed germination and vigor traits of three maize hybrids, Pioneer 3025, Pioneer 70 and Baber at Agronomy research laboratory, University of Agriculture, Peshawar, Pakistan. The experiment was laid in completely randomized design (CRD) and was replicated thrice. The treatments included control treatment (T1) unsoaked/dry seed, (T2) hydropriming with distilled water for 24 hrs, (T3) halo priming treatments with NaCl (3% solution) for 24 hrs, (T4) osmopriming with PEG-6000 for 24 hrs and (T5), hormonal priming with GA3 for 24 hrs. The results showed that seed invigoration treatment with gibberellic acid (GA3) PEG-6000 and hydropriming with distilled water for 24 hrs gave higher germination, decreased days to 50% germination, increased shoot length, root length, seedling fresh and dry weight, as compared to halo priming with NaCl and control treatment. It is concluded that seed invigoration with GA3, osmopriming with PEG-6000 and hydropriming with distilled water for 24 hrs serve as an appropriate treatment for accelerating the emergence and growth parameters of maize hybrid. Pioneer 3025 showed its superiority over other cultivars in all the studied parameters.