A Note on Function Space and Boundedness of the General Fractional Integral in Continuous Time Random Walk
Fan Qin, Guo–Cheng Wu, Hui Fu
Abstract
Abstract The general fractional calculus becomes popular in continuous time random walk recently. However, the boundedness condition of the general fractional integral is one of the fundamental problems. It wasn’t given yet. In this short communication, the classical norm space is used, and a general boundedness theorem is presented. Finally, various long–tailed waiting time probability density functions are suggested in continuous time random walk since the general fractional integral is well defined.
Topics & Concepts
MathematicsRandom walkFractional calculusNorm (philosophy)Space (punctuation)Daniell integralMathematical analysisApplied mathematicsIntegral equationSingular integralStatisticsPhilosophyLawPolitical scienceLinguisticsFractional Differential Equations SolutionsMathematical and Theoretical AnalysisStatistical Mechanics and Entropy