Coefficient of restitution in fractional viscoelastic compliant impacts using fractional Chebyshev collocation

FMNEICS: fractional Meyer neuro-evolution-based intelligent computing solver for doubly singular multi-fractional order Lane–Emden system

“…: V,-vol i-Kober operators (Diethelm and Ford 2002), Caputo operator (Momani and Ibrahim 2008), Grnwald-Letnikov operator (Bonilla et al 2007), and Weyl-Riesz operator (Ibrahim and Momani 2007). Keeping in view the significance of these fractional operators, the interest of researchers grow considerably for investigation in different fields such as application in the modeling of fractional viscoplasticity (Sumelka 2014;Diethelm and Freed 1999), edge detection in road obstacle (Daou et al 2020), earth system dynamical studies (Zhang et al 2017a), surface-volume reaction problem (Evans et al 2017), thorough behaviors analysis in the real materials (Torvik and Bagley 1984), electromagnetic theory developed on fractional calculus concepts (Engheia 1997), modeling of viscoelastic systems (Matlob and Jamali 2019), mathematical models of nanofluidic studies (Aman et al 2018), fractal LC-electric circuit modeled (Yang et al 2017), control systems (Baleanu et al 2011;Dabiri et al 2018Dabiri et al ,2017aDabiri and Butcher 2019), physics (Hilfer 2000;Dabiri et al 2017b), engineering dynamics (Moghadam et al xxxx;Bǎleanu et al 2019;Uchaikin 2013), and many others (Sun et al 2018;Mishra et al 2019;Zhao et al 2018;Zhang et al 2017b;Jaradat et al 2018).…”

A numerical study of fractional rheological models and fractional Newell-Whitehead-Segel equation with non-local and non-singular kernel

“…In the end of nineteenth century basic theory of fractional calculus was developed with the studies of Liouville, Grünwald, Letnikov, and Riemann. It has been shown that fractional derivative operators are useful in describing dynamical processes with memory or hereditary properties such as creep or relaxation processes in viscoelastoplastic materials [3] , [4] , impact problem [5] , plasma physics [1] , diffusion process models [6] , [7] , [8] , [9] , chaotic systems [10] , control problems [11] , [12] , dynamics modeling of coronavirus (2019-nCov) [13] , etc .…”

The minimax approach for a class of variable order fractional differential equation

“…Recently, the fractional differential equations have been used to model and characterize different processes in physical science and engineering such as control theory, bioengineering, signal processing, biology, finance, visco‐plasticity, vibration, and circuit theory . Therefore, the numerical methods for these equations have undergone fast growth in recent years.…”