Fractional trajectories: Decorrelation versus friction

Beig, Mirza Tanweer Ahmad; Turalska, Malgorzata; West, Bruce J.; Grigolini, Paolo

doi:10.1016/j.physa.2013.07.028

Cited by 10 publications

(10 citation statements)

References 34 publications

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“…Thus it is of interest to investigate whether the fractional analog of the above well known equations retain its mathematical structures or not. It is appropriate to mention that Svenkeson et al [28] have demonstrated a general connection between fractional calculus and the process of subordination. The significance of this connection is that a single fractional trajectory obtained as the solution to a fractional equation of motion can be interpreted as an average over an ensemble of stochastically evolving ordinary trajectories [29].…”

Section: Introductionmentioning

confidence: 99%

Approximate Analytical Solution of Two Coupled Time Fractional Nonlinear Schrödinger Equations

Bakkyaraj

Sahadevan

2015

Int. J. Appl. Comput. Math

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In this article, we consider the well known nonlinear Schrödinger equation (NLS) with fractional time derivative and derive its approximate analytical solution using the homotopy analysis method (HAM). We also applied HAM to two coupled time fractional NLS and constructed its approximate solution. The question of convergence of the obtained solution is discussed. The obtained approximate analytical periodic wave solution, solitary wave solution and the effect of time fractional order α are shown graphically.

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Section: Introductionmentioning

confidence: 99%

Approximate Analytical Solution of Two Coupled Time Fractional Nonlinear Schrödinger Equations

Bakkyaraj

Sahadevan

2015

Int. J. Appl. Comput. Math

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“…(19) takes into account that the number of possible events may range from the no-event case to that of infinitely many events. The conditions necessary for this result to occur are discussed by Svenkenson et al [12].…”

Section: Subordination and Fractional Dynamicsmentioning

confidence: 93%

Fractional Stochastic Individuals

Turalska¹,

West²

2013

Self Cite

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The decision making model (DMM) [1,2] has been shown to generate phase transitions, to be topologically complex and to manifest temporal complexity through size-dependent random fluctuations in the switching times between the two critical states of consensus. These properties are entailed by the fundamental assumption that the network elements in the DMM imperfectly imitate one another. The process of subordination establishes that a single network element can be described by a fractional master equation whose analytic solution yields the observed autocorrelation function obtained by numerical integration of the DMM to a high degree of accuracy.

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“…To generalize this description, we introduce the notion of subordination. This notion implies the existence of two ideas of time, as explained by Svenkeson et al [121]. One is the operational time, τ , which is the internal time of a single individual, with an individual generating the ordinary dynamics of a non-fractional system, such as given by Equation (9).…”

Section: Subordinationmentioning

confidence: 99%

“…Svenkeson et al [121] point out that in operational time, an individual's behavior can appear deterministic, but to an experimenter observing the individual, their temporal behavior can appear to erratically grow in time, then abruptly to freeze in different states for extended time intervals. Due to the random nature of the evolution of the individual in chronological time, the subordination process involves an ensemble average over many individuals, each evolving according to its own internal clock, independently of one another.…”

Section: Subordinationmentioning

confidence: 99%

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A Fractional Probability Calculus View of Allometry

West¹

2014

Systems

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The scaling of respiratory metabolism with body size in animals is considered by many to be a fundamental law of nature. An apparent corollary of this law is the scaling of physiologic time with body size, implying that physiologic time is separate and distinct from clock time. However, these are only two of the many allometry relations that emerge from empirical studies in the physical, social and life sciences. Herein, we present a theory of allometry that provides a foundation for the allometry relation between a network function and the size that is entailed by the hypothesis that the fluctuations in the two measures are described by a scaling of the joint probability density. The dynamics of such networks are described by the fractional calculus, whose scaling solutions entail the empirically observed allometry relations.

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Fractional trajectories: Decorrelation versus friction

Cited by 10 publications

References 34 publications

Approximate Analytical Solution of Two Coupled Time Fractional Nonlinear Schrödinger Equations

Approximate Analytical Solution of Two Coupled Time Fractional Nonlinear Schrödinger Equations

Fractional Stochastic Individuals

A Fractional Probability Calculus View of Allometry

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