The computational work and storage of numerically solving the time fractional PDEs are
generally huge for the traditional direct methods since they require total memory and work …

In the present work, first, a new fractional numerical differentiation formula (called the L1-2
formula) to approximate the Caputo fractional derivative of order α (0< α< 1) is developed. It …

Fractional nonlinear models involving the underlying mechanisms of numerous complicated
physical phenomena arising in nature of real world have been taken major place of research …

In this paper, we present a new definition of fractional-order derivative with a smooth kernel
based on the Caputo–Fabrizio fractional-order operator which takes into account some …

In this study a new framework for solving three-dimensional (3D) time fractional diffusion
equation with variable-order derivatives is presented. Firstly, a θ-weighted finite difference …

The conformable fractional derivative was proposed by R. Khalil et al. in 2014, which is
natural and obeys the Leibniz rule and chain rule. Based on the properties, a class of time …

In this article, we consider the exact solutions of the Hunter-Saxton and Schrödinger
equations defined by Atangana's conformable derivative using the general Kudryashov …

The generalized Riccati equation (GRE) together with the basic simplest equation method
(SEM) is investigated to deal with the nonlinear fractional differential equations. This method …

Starting with an introduction to fractional derivatives and numerical approximations, this
book presents finite difference methods for fractional differential equations, including time …

Accurate estimation of state of health (SOH) of lithium-ion batteries is crucial to ensure that
the battery management system stably runs. Extraction of characteristic parameters (CPs) is …