(R2028) A Brief Note on Space Time Fractional Order Thermoelastic Response in a Layer

In this study, a one-dimensional layer of a solid is used to investigate the exact analytical solution of the heat conduction equation with space-time fractional order derivatives and to analyze its associated thermoelastic response using a quasi-static approach. The assumed thermoelastic problem was subjected to certain initial and boundary conditions at the initial and final ends of the layer. The memory effects and long-range interaction were discussed with the help of the Caputo-type fractional-order derivative and finite Riesz fractional derivative. Laplace transform and Fourier transform techniques for spatial coordinates were used to investigate the solution of the temperature distribution and stress functions. Numerical investigations are also shown graphically for non-dimensional temperature and stress for different space and time fractional derivative values, respectively. In addition, some applicable limiting cases are discussed for standard equations, such as wave equation, Laplace equation, and diffusion equation

Complex boundary value problems of nonlinear differential equations: Theory, computational methods, and applications

Editorial to the theme Complex Boundary Value Problems of Nonlinear Differential Equations: Theory, Computational Methods, and Application

A New Grünwald-Letnikov Derivative Derived from a Second-Order Scheme

A novel derivation of a second-order accurate Grünwald-Letnikov-type approximation to the fractional derivative of a function is presented. This scheme is shown to be second-order accurate under certain modifications to account for poor accuracy in approximating the asymptotic behavior near the lower limit of differentiation. Some example functions are chosen and numerical results are presented to illustrate the efficacy of this new method over some other popular choices for discretizing fractional derivatives