Cauchy Problem for a Stochastic Fractional Differential Equation with Caputo-Ito Derivative

被引：1
|
作者：
Sanchez-Ortiz, Jorge [1 ]
Lopez-Cresencio, Omar U. [1 ]
Ariza-Hernandez, Francisco J. [1 ]
Arciga-Alejandre, Martin P. [1 ]
机构：
[1] Univ Autonoma Guerrero, Fac Matemat, Av Lazaro Cardenas S-N Cd, Chilpancingo 39087, Guerrero, Mexico
来源：
MATHEMATICS | 2021年 / 9卷 / 13期
关键词：
brownian motion; Caputo-Ito derivative; Ito process; existence; uniqueness; CALCULUS;
D O I：
10.3390/math9131479
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this note, we define an operator on a space of Ito processes, which we call Caputo-Ito derivative, then we considerer a Cauchy problem for a stochastic fractional differential equation with this derivative. We demonstrate the existence and uniqueness by a contraction mapping argument and some examples are given.
引用
收藏
页数：10
相关论文
共 50 条
  • [31] Application of Avery-Peterson fixed point theorem to nonlinear boundary value problem of fractional differential equation with the Caputo's derivative
    Liu, Yang
    COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2012, 17 (12) : 4576 - 4584
  • [32] Cauchy Problem for a Fractional Parabolic Equation with the Advection
    Li Xitao
    Xu Meng
    Zhou Shulin
    JOURNAL OF PARTIAL DIFFERENTIAL EQUATIONS, 2018, 31 (03): : 252 - 273
  • [33] An Extension of the Picard Theorem to Fractional Differential Equations with a Caputo-Fabrizio Derivative
    Marasi, H. R.
    Joujehi, A. Soltani
    Aydi, H.
    JOURNAL OF FUNCTION SPACES, 2021, 2021
  • [34] Existence and Stability for Fractional Differential Equations with a ψ-Hilfer Fractional Derivative in the Caputo Sense
    He, Wenchang
    Jin, Yuhang
    Wang, Luyao
    Cai, Ning
    Mu, Jia
    MATHEMATICS, 2024, 12 (20)
  • [35] A New Result for Fractional Differential Equation With Nonlocal Initial Value Using Caputo-Fabrizio Derivative
    Mokhtary, Z.
    Ghaemi, M. B.
    Salahshour, S.
    FILOMAT, 2022, 36 (09) : 2881 - 2890
  • [36] A sufficient condition of viability for fractional differential equations with the Caputo derivative
    Girejko, Ewa
    Mozyrska, Dorota
    Wyrwas, Malgorzata
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2011, 381 (01) : 146 - 154
  • [37] THEORY AND ANALYSIS OF PARTIAL DIFFERENTIAL EQUATIONS WITH A ψ-CAPUTO FRACTIONAL DERIVATIVE
    Vivek, D.
    Elsayed, E. M.
    Kanagarajan, K.
    ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, 2019, 49 (04) : 1355 - 1370
  • [38] BOUNDARY VALUE PROBLEM OF CAPUTO FRACTIONAL DIFFERENTIAL EQUATIONS OF VARIABLE ORDER
    Refice, A.
    Ozer, O.
    Souid, M. S.
    TWMS JOURNAL OF APPLIED AND ENGINEERING MATHEMATICS, 2023, 13 (03): : 1053 - 1067
  • [39] BOUNDARY VALUE PROBLEM FOR NONLINEAR CAPUTO-HADAMARD FRACTIONAL DIFFERENTIAL EQUATION WITH HADAMARD FRACTIONAL INTEGRAL AND ANTI-PERIODIC CONDITIONS
    Boutiara, Abdelatif
    Benbachir, Maamar
    Guerbati, Kaddour
    FACTA UNIVERSITATIS-SERIES MATHEMATICS AND INFORMATICS, 2021, 36 (04): : 735 - 748
  • [40] On the Existence and Stability of Boundary Value Problem for Differential Equation with Hilfer-Katugampola Fractional Derivative
    Elsayed, E. M.
    Harikrishnan, S.
    Kanagarajan, K.
    ACTA MATHEMATICA SCIENTIA, 2019, 39 (06) : 1568 - 1578
12345