Fractional Dynamics in Bioscience and Biomedicine and the Physics of Cancer

Abstract

Almost all phenomena and structures in nature exhibit some degrees of fractionality or fractality. Fractional calculus and fractal theory are two interrelated concepts. In this article we study the memory effects in nature and particularly in biological structures. Based on this fact that natural way to incorporate memory effects in the modeling of various phenomena and dealing with complexities is using of fractional calculus, in this article we present different examples in various branch of science from cosmology to biology and we investigate this idea that are we able to describe all of such these phenomena using the well-know and powerful tool of fractional calculus. In particular we focus on fractional calculus approach as an effective tool for better understanding of physics of living systems and organism and especially physics of cancer.Keywords: Fractional Dynamics; Memory Effect; Biological Structures; Physics of Cancer IntroductionThe concept of memory effect plays an important role in a large number of phenomena in different contexts and systems from biological structures to cosmological phenomena. For instance: memory effects in nanoscale systems [1,2], optical memory effect [3], gravitational and cosmological memory effect (which means: the induction of a permanent change in the relative separation of the test particles when gravitational radiation passes through a configuration of test particles that make up a gravitational wave detector) [4], memory effects in gene regulatory networks [5], memory effects in economics [6] have been investigated. In addition other kinds of memory effect including: shape memory effect [7][8][9][10], magnetic shape memory effect [11] and temperature memory effect [12] have been also considered in recent years. In all above mentioned references authors have used the standard calculus, however nowadays it is well-known that a natural way to incorporate memory effects in the modeling of various phenomena is using of fractional calculus. On the other hand almost all phenomena and structures in nature exhibit some degrees and levels of fractionality or fractality (low or high level or something between them), also nowadays it is well-known that there is a close relation between fractality and fractionality. In this work we investigate this idea that are we able to describe all of such these phenomena using the well-know and powerful tool of fractional calculus. Therefore for this purpose in the following, concepts of fractality and fractional dynamics are briefly reviewed respectively in Sec. 2.Then in Sec. 3 we introduce fractional calculus as a powerful tool for modeling of memory effects in different context and we present some important applications. At last, in Sec. 4, we will present some conclusions.

The Fractal Tapestry of Life: II Entailment of Fractional Oncology by Physiology Networks

“…The prequel closed with a suggestion that the FC is a systematic way to incorporate spatial inhomogeneity into describing how information is transported across a complex dynamic network. That suggestion was augmented by another involving memory effects in physiologic networks being generic (Goldberger et al, 2002) and the FC was also pointed out by Nasrolahpour (Nasrolahpour, 2017) as being the natural way to incorporate memory effects into the modeling of various complex phenomena including the growth of cancer tumors. He (Nasrolahpour, 2017) proposed a new model which is a member of a class of simple models that have been extensively used to describe the growth of stem and cancer cells.…”

“…Therefore, since the effects of spatial heterogeneity and memory are frequently observed in biological, social, and artificial networks (Magin, 2016;Meerschaert et al, 2017), the application of FC in the domain of complex networks is a natural step toward providing novel analytical tools that are capable of addressing research questions arising in the field of medicine, such as fractional dynamics (FD). For example, FD has been used to model the complex dynamics in biological tissue (Magin, 2010) and biomedicine (Nasrolahpour, 2017;Nasrolahpour, 2018), as well as in the growth of cancer cells (Valentim et al, 2021), the signal decay in MRIs (Magin, 2016), and finally in the bizarre statistical fluctuations in dilute suspensions of algae and bacteria (Zaid et al, 2011), to name a few applications that are subsequently discussed.…”

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“…Open Access L natural exponential function has been considered as a fundamental function of natural science and in particular biology up to now, so that many phenomena could be described using it and now scientist are able to think that with such this new framework (i.e. fractional differential equations and their solutions in terms of Mittag-Leffler functions) they can find many new results and information about biological and biomedical phenomena [2,3].…”

Qualitative Analysis of Metformin Drug Administration in Caputo Setting

“…In the G-C, non-local operators are being used to determine a memory and history of a process. The G-C has recently been used to explain a variety of challenging topics in applied sciences and engineering [18][19][20]. Researchers developed mathematical theories to mimic the complexity of nature using the tools from G-C and studied the memory mechanism, heredity aspects of a physical processes [21][22][23].…”