Year 2020, Volume 49 , Issue 1, Pages 282 - 293 2020-02-06

On initial value problem of random fractional differential equation with impulses

Vu HO [1] , Hoa NGO [2]


In this paper, we prove the existence and uniqueness of solution for random fractional differential equation with impulses via Banach fixed point theorem and Schauder fixed point theorem. Moreover, the continuous dependence of the solution on the initial data is investigated.
Random fractional differential equation with impulses, second-order stochastic processes, mean square continuous solution
  • [1] B. Bayour and D. Torres, Existence of solution to a local fractional nonlinear differential equation, J. Comput. Appl. Math., 312, 127–133, 2017.
  • [2] A. Bharucha-Reid, Random integral equations, Academic Press, New York, 1972.
  • [3] A. El-Sayed, The mean square riemann-liouville stochastic fractional derivative and stochastic fractional order differential equation, Math. Sci. Res. J., 9, 142–150, 2005.
  • [4] A. El-Sayed, On the stochastic fractional calculus operators, J. Frac. Calc. Appl., 6, 101–109, 2015.
  • [5] F. Hafiz, The fractional calculus for some stochastic processes, Stoch. Anal. Appl., 22, 507–523, 2004.
  • [6] F. Hafiz, A. El-Sayed and M. El-Tawil, On a stochastic fractional calculus, Frac. Calc. Appl. Anal., 4, 81–90, 2001.
  • [7] A. Kilbas, H. Srivastava and J. Trujillo, Theory and applications of fractional differential equations, Volume 204, North-Holland Mathematics Studies, Elsevier Science Inc., 2006.
  • [8] G. Ladde and V. Lakshmikantham, Random differential inequalities, Academic Press, New York, 1980.
  • [9] V. Lakshmikantham, S. Leela and J. V. Devi, Theory of fractional dynamic systems, Cambridge Scientific Publishers, 2009.
  • [10] V. Lupulescu and S. Ntouyas, Random fractional differential equations, Int. Elec. J. Pure Appl. Math., 4, 119–136, 2012.
  • [11] V. Lupulescu, D. O’Regan and G. ur Rahman, Existence results for random fractional differential equations, Opuscula Mathematica, 34, 813–825, 2014.
  • [12] Z.-D. Mei, J.-G. Peng and J.-H. Gao, Existence and uniqueness of solutions for nonlinear general fractional differential equations in banach spaces, Indagat. Math., 26, 669–678, 2015.
  • [13] K. Miller and B. Ross, An introduction to the fractional calculus and fractional differential equations, Wiley-Interscience, 1993.
  • [14] Z. Shuorui and S. Jitao, On existence and uniqueness of random impulsive differential equations, J. Syst. Sci. Complex., 29, 300–314, 2016.
  • [15] T. Soong, Random differential equations in science and engineering, Academic Press.
  • [16] N. Tobias and R. Florian, Random differential equations in scientific computing, De Gruyter Open, Berlin, 2013.
  • [17] H. Vu, Random fractional functional differential equations, Int. J. Nonlin. Anal. Appl., 7, 253–267, 2016.
  • [18] H. Vu, N. Phung and N. Phuong, On fractional random differential equations with delay, Opuscula Mathematica, 36, 541–556, 2016.
  • [19] D. Yang and J. Wang, Non-instantaneous impulsive fractional-order implicit differential equations with random effects, Stoch. Anal. Appl., 35, 719–741, 2017.
  • [20] Y. Zou and G. He, On the uniqueness of solutions for a class of fractional differential equations, Appl. Math. Lett., 74, 68–73, 2017.
Primary Language en
Subjects Mathematics
Journal Section Mathematics
Authors

Orcid: 0000-0001-7274-6096
Author: Vu HO
Institution: Banking University of Ho Chi Minh City
Country: Vietnam


Orcid: 0000-0002-4603-4682
Author: Hoa NGO
Institution: Ton Duc Thang University
Country: Vietnam


Dates

Publication Date : February 6, 2020

Bibtex @research article { hujms546989, journal = {Hacettepe Journal of Mathematics and Statistics}, issn = {2651-477X}, eissn = {2651-477X}, address = {}, publisher = {Hacettepe University}, year = {2020}, volume = {49}, pages = {282 - 293}, doi = {10.15672/hujms.546989}, title = {On initial value problem of random fractional differential equation with impulses}, key = {cite}, author = {HO, Vu and NGO, Hoa} }
APA HO, V , NGO, H . (2020). On initial value problem of random fractional differential equation with impulses. Hacettepe Journal of Mathematics and Statistics , 49 (1) , 282-293 . DOI: 10.15672/hujms.546989
MLA HO, V , NGO, H . "On initial value problem of random fractional differential equation with impulses". Hacettepe Journal of Mathematics and Statistics 49 (2020 ): 282-293 <https://dergipark.org.tr/en/pub/hujms/issue/52287/546989>
Chicago HO, V , NGO, H . "On initial value problem of random fractional differential equation with impulses". Hacettepe Journal of Mathematics and Statistics 49 (2020 ): 282-293
RIS TY - JOUR T1 - On initial value problem of random fractional differential equation with impulses AU - Vu HO , Hoa NGO Y1 - 2020 PY - 2020 N1 - doi: 10.15672/hujms.546989 DO - 10.15672/hujms.546989 T2 - Hacettepe Journal of Mathematics and Statistics JF - Journal JO - JOR SP - 282 EP - 293 VL - 49 IS - 1 SN - 2651-477X-2651-477X M3 - doi: 10.15672/hujms.546989 UR - https://doi.org/10.15672/hujms.546989 Y2 - 2018 ER -
EndNote %0 Hacettepe Journal of Mathematics and Statistics On initial value problem of random fractional differential equation with impulses %A Vu HO , Hoa NGO %T On initial value problem of random fractional differential equation with impulses %D 2020 %J Hacettepe Journal of Mathematics and Statistics %P 2651-477X-2651-477X %V 49 %N 1 %R doi: 10.15672/hujms.546989 %U 10.15672/hujms.546989
ISNAD HO, Vu , NGO, Hoa . "On initial value problem of random fractional differential equation with impulses". Hacettepe Journal of Mathematics and Statistics 49 / 1 (February 2020): 282-293 . https://doi.org/10.15672/hujms.546989
AMA HO V , NGO H . On initial value problem of random fractional differential equation with impulses. Hacettepe Journal of Mathematics and Statistics. 2020; 49(1): 282-293.
Vancouver HO V , NGO H . On initial value problem of random fractional differential equation with impulses. Hacettepe Journal of Mathematics and Statistics. 2020; 49(1): 293-282.