Abstract
AbstractThe 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.
Funder
National Natural Science Foundation of China
Sichuan Youth Science and Technology Foundation
Publisher
Springer Science and Business Media LLC
Subject
Mathematical Physics,Statistical and Nonlinear Physics
Reference16 articles.
1. Osler, T.J.: Leibniz rule for fractional derivatives generalized and an application to infinite series. SIAM J. Appl. Math. 18, 658–674 (1970)
2. Samko, S.G., Kilbas, A.A., Marichev, O.I.: Fractional integrals and derivatives: theory and applications. CRC Press (1993)
3. Kilbas, A.A., Srivastava, H.M., Trujillo, J.J.: Theory and Applications of Fractional Differential Equations. Elsevier Science B. V, Amsterdam (2006)
4. Almeida, R.: A Caputo fractional derivative of a function with respect to another function. Commun. Nonlinear Sci. Numer. Simulat. 44, 460–481 (2017)
5. Fahad, H.M., Rehman, M.U., Fernandez, A.: On Laplace transforms with respect to functions and their applications to fractional differential equations. Math. Method. Appl. Sci. (2021). https://doi.org/10.1002/mma.7772
Cited by
51 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献