The solution of direct and inverse fractional advection–dispersion problems by using orthogonal collocation and differential evolution

Solution of Fractional Optimal Control Problems by using orthogonal collocation and Multi-objective Optimization Stochastic Fractal Search

“…From the engineering perspective, fractional orders can be interpreted as parameters that influence the behavior of systems. In this case, the corresponding models can be used to represent phenomena observed in nature and to evaluate the influence of fractional orders on phenomenological profiles (Lobato et al 2019).…”

“…The study of fractional calculus arises by the end of the seventeenth century. In the specialized literature, various contributions can be found, such as those on chemistry (Kirchner et al 2000), finance (Sabatelli et al 2002), hydrology (Schumer et al 2003), biology (Magin 2006), viscoelasticity (Larsson et al 2015), chaos synchronization (Su et al 2016), robotics (Kumar and Rana 2017), anomalous diffusion (Zhang et al 2017), anomalous heat-diffusion problems (Yang et al 2017a), advection-dispersion problems (Yuan et al 2016;Zhang, 2018;Li and Rui 2018), fractional Boussinesq equation (Yang et al 2017b), diffusion equations (Yang et al 2018), anomalous advection-dispersion equations (Liang et al 2018), solution of direct and inverse fractional advection-dispersion problem (Lobato et al 2019), and anomalous diffusion equations (Yang et al 2019).…”

Solution of mass-spring-damper fractional systems using Caputo derivative and orthogonal collocation

“…The current issue and full text archive of this journal is available on Emerald Insight at: https://www.emerald.com/insight/0264-4401.htm (Liang et al, 2018), inverse fractional advection-dispersion problem (Lobato et al, 2019), anomalous diffusion equations (Yang et al, 2019), risk theory (Constantinescu et al, 2019), HIV dynamics (Wasques et al, 2020), solution of mathematical equations using spline collocation methods (Zahra et al, 2020) and Langevin equation (Yang et al, 2020).…”

“…The study of Fractional Differential Equations (FDEs) configures a theme of great interest in science due to the capacity of this type of model to represent a number of phenomena found in nature (Lobato et al , 2019). In this sense, the fractional calculation comes to be understood as a generalization of classical calculation where the integrals and derivatives may have noninteger order (Stanislavsky, 2004).…”

“…In the past decades, different applications considering models represented by fractional order in different fields of science have been published in the literature. Among them, we can cite studies on chemistry (Kirchner et al , 2000), finance (Sabatelli et al , 2002; Bohner and Hatipoğlu, 2018, 2019), hydrology (Schumer et al , 2003), biology (Magin, 2006), viscoelasticity (Larsson et al , 2015), eigenvalue problem (Jin and Liu, 2016), robotics (Kumar and Rana, 2017), anomalous diffusion (Zhang et al , 2017), anomalous heat-diffusion problems (Yang et al , 2017a), advection-dispersion problems (Yuan et al , 2016; Zhang, 2018; Li and Rui, 2018), fractional Boussinesq equation (Yang et al , 2017b), diffusion equations (Yang et al , 2018; Shi et al , 2020), chaos synchronization (Su et al , 2018), anomalous advection-dispersion equations (Liang et al , 2018), inverse fractional advection-dispersion problem (Lobato et al , 2019), anomalous diffusion equations (Yang et al , 2019), risk theory (Constantinescu et al , 2019), HIV dynamics (Wasques et al , 2020), solution of mathematical equations using spline collocation methods (Zahra et al , 2020) and Langevin equation (Yang et al , 2020).…”