Fractional Dynamics for Coupled CTRW Optimal Random Search Algorithm

Fractional mathematical oncology: cancer-related dynamics under an interdisciplinary viewpoint

“…Other studies embrace treatment optimization methods (UCAR; ÖZDEMIR; AL-TUN, 2019; KHAJANCHI; NIETO, 2019), control in invasion systems (MANIMARAN et al, 2019;DAI;LIU, 2019), bioengineering (IONESCU et al, 2017, and general tumor growth (REN;YU;CHEN, 2018;SOWNDARRAJAN et al, 2019;FARAYOLA et al, 2020). From aforementioned studies, one can note the contemporary interest of the scientific community towards mathematical tools that suitably describe oncological models, improve the understanding of tumor mechanics and evolution, and expand diagnostic options and treatment routines.…”

“…For their many remarkable characteristics, fractional models have been increasingly chosen and successfully applied in signal processing (MILJKOVIĆ et al, 2017), thermoacoustics (VALENTIM, 2018), economy , robotics (LEYDEN; GOOD-WINE, 2016), viscoelasticity (DAVID; KATAYAMA, 2013), chemical kinetics (SINGH; KUMAR; BALEANU, 2017), electromagnetism (MESCIA; BIA; CARATELLI, 2019), agricultural computing ), traffic control (KUMAR et al, 2018, among other areas (DAVID; MAINARDI, 2018;O'REGAN;BALACHANDRAN, 2010). In fact, what could be coined as "fractional mathematical oncology" already exists, with many recent studies deploying non-integer calculus to deal with cancer-related topics including chemotherapy, radiotherapy and immunotherapy dynamics (UCAR; ÖZDEMIR; ALTUN, 2019;YILDIZ;ARSHAD;BALEANU, 2018;FARAYOLA et al, 2020;KHAJANCHI;NIETO, 2019), numerical solution and control for invasion systems (MANIMARAN et al, 2019;DAI;LIU, 2019), bioengineering (IONESCU et al, 2017), and tumor growth (SOWNDARRAJAN et al, 2019;SOLÍS-PÉREZ;GÓMEZ-AGUILAR;ATANGANA, 2019ATANGANA, , 2019REN;YU;CHEN, 2018;BOLTON et al, 2015). The increasing number of studies in this area might support fractional calculus as alternative reductionist phenomenological modeling (approach) to further investigate early avascular general tumor growth governed by ODEs.…”