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This book discusses various novel analytical and numerical methods for solving partial and fractional differential equations. Moreover, it presents selected numerical methods for solving stochastic point kinetic equations in nuclear reactor dynamics by using Euler–Maruyama and strong-order Taylor numerical methods. The book also shows how to arrive at new, exact solutions to various fractional differential equations, such as the time-fractional Burgers–Hopf equation, the (3+1)-dimensional time-fractional Khokhlov–Zabolotskaya–Kuznetsov equation, (3+1)-dimensional time-fractional KdV–Khokhlov–Zabolotskaya–Kuznetsov equation, fractional (2+1)-dimensional Davey–Stewartson equation, and integrable Davey–Stewartson-type equation.
Mathematical Preliminaries
New Approaches for Decomposition Method for the Solution of Differential Equations
Numerical Solution of Fractional Differential Equations by Using New Wavelet Operational Matrix of General Order
Numerical Solutions of Riesz Fractional Partial Differential Equations
New Exact Solutions of Fractional-Order Partial Differential Equations
New Exact Traveling Wave Solutions of the Coupled Schrödinger–Boussinesq Equations and Tzitzéica-Type Evolution Equations
New Techniques on Fractional Reduced Differential Transform Method
A Novel Approach with Time-Splitting Fourier Spectral Method for Riesz Fractional Differential Equations
Numerical Simulation of Stochastic Point Kinetics Equation in the Dynamical System of Nuclear Reactor