Role and Function of Eethylene Response Factor in Different Plants under Multiple Biotic and Abiotic Stresses

These stresses effect crop production and quality, thus result is in economic lose and food insecurity. Many factors play vital role in regulating growth of plants along with developmental pathways during biotic and abiotic stresses. Transcription factors are proteins that control physiological, developmental and stress responses in plants. Ethylene response factors belong to the biggest family of transcription factors, known to participate in various stress tolerance like drought, heat, salt and cold. They are significant regulators of plant gene expression. The objective of this review is to present how ethylene response factor family proteins became the focus of stress tolerance as well as the development and growth of plants.

Spline Solutions for Some Fractional Order Boundary Value Problems

In this thesis, the spline solutions to some fractional order boundary value problems have been proposed using different spline collocation techniques. The Caputo’s definition for fractional order derivatives is used, as it allows imposing the boundary constraint(s) in terms of integer order derivative(s). An efficient technique based on non-polynomial quintic spline functions, comprised of a trigonometric part and polynomial part, has been developed for solving fourth order fractional boundary value problems involving product terms. The C¥ differentiability of the trigonometric part of non-polynomial spline compensates for the loss of smoothness inherent in polynomial spline. The second and fourth order convergence of the presented algorithm has been discussed in detail. Moreover, the approximate solutions of three very important time fractional models, advection-diffusion equation, Allen-Cahn equation and diffusion-wave equation, have been studied by means of redefined and modified forms of cubic B-spline functions. The Caputo time-fractional derivatives have been discretized by finite difference formulations whereas B-spline functions are used for spatial discretization. The unconditional stability and theoretical convergence of proposed numerical algorithms have been proved rigorously. Some test examples have been considered for numerical experiments. The computational results are in line with theoretical expectations and exhibit a superior agreement with the analytical exact solutions as compared to the existing techniques.