Fractional neutral stochastic integrodifferential equations with Caputo fractional derivative: Rosenblatt process, Poisson jumps and Optimal control

• Ravikumar, K. ; Ramkumar, K. ; Ahmed, Hamdy ^[1]
  1. [1] El-Shorouk Academy.
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 42, Nº. 3, 2023, págs. 549-570
• Idioma: inglés
• DOI: 10.22199/issn.0717-6279-4329
• Enlaces
  • Texto completo
• Resumen

  • The objective of this paper is to investigate the existence of mild solutions and optimal controls for a class of fractional neutral stochastic integrodifferential equations driven by Rosenblatt process and Poisson jumps in Hilbert spaces. First we establish a new set of sufficient conditions for the existence of mild solutions of the aforementioned fractional systems by using the successive approximation approach.

    The results are formulated and proved by using the fractional calculus, solution operator and stochastic analysis techniques. The existence of optimal control pairs of system governed by fractional neutral stochastic differential equations driven by Rosenblatt process and poisson jumps is also been presented. An example is provided to illustrate the theory.

• Referencias bibliográficas
  • A. A. Kilbas, H. M. Srivastava and J. J. Trujillo, Theory and Applications of Fractional Differential Equations. Amsterdam: Elsevier Science,...
  • I. Podlubny, Fractional Differential Equations. London: Academic Press, 1999.
  • F. Biagini, Y. Hu and B. Oksendal, T. Zhang, Stochastic Calculus for Fractional Brownian Motion and Applications. London: Springer, 2008.
  • X. Mao, Stochastic Differential Equations and Applications. Chichester: Horwood, 1997.
  • M. A. Ouahra, B. Boufoussi and E. Lakhel, “Existence and stability for stochastic impulsive neutral partial differential equations driven...
  • G. D. Prato and J. Zabczyk, Stochastic Equations in Infinite Dimensions. London: Cambridge University Press, 2014.
  • H. M. Ahmed, “Semilinear neutral fractional stochastic integrodifferential equations with nonlocal conditions”, Journal of Theoretical Probability,...
  • A. Anguraj and K. Ravikumar, “Existence and stability results for impulsive stochastic functional integrodifferential equations with Poisson...
  • J. Luo and T. Taniguchi, “The existence and uniqueness for non-Lipschitz stochastic neutral delay evolution equations driven by Poisson jumps”,...
  • P. Tamilalagan and P. Balasubramaniam, Existence results for semilinear fractional stochastic evolution inclusions driven by Poisson jumps,...
  • F. A. Rihan, C. Rajivganthi and P. Muthukumar, “Fractional stochastic differential equations with Hilfer fractional derivative: Poisson jumps...
  • P. Balasubramaniam, S. Saravanakumar and K. Ratnavelu, “Study a class of Hilfer fractional stochastic integrodifferential equations with Poisson...
  • H. M. Ahmed and M. M. El-Borai, “Hilfer fractional stochastic integrodifferential equations”, Applied Mathematics and Computation, vol. 331,...
  • F. Biagini, Y. Hu, B. Oksendal and T. Zhang, Stochastic calculus for fractional Brownian motion and applications. Springer Science & Business...
  • C. A. Tudor, “Analysis of the Rosenblatt process”. ESAIM: Probability and Statistics, vol. 12, pp. 230-257, 2008. https://doi.org/10.1051/ps:2007037
  • M. Maejima and C. A. Tudor, “On the distribution of the Rosenblatt process”, Statistics & Probability Letters, vol. 83, no. 6, pp. 1490-1495,...
  • L. Urszula and H. Schattler, “Antiangiogenic therapy in cancer treatment as an optimal control proble”, SIAM Journal on Control and Optimization,...
  • I. Area, F. NdaÏrou, J. J. Nieto, C. J. Silva and D. F. Torres, “Ebola model and optiimal control with vaccination constraints”, Journal of...
  • P. Tamilalagan and P. Balasubramniam, “The solvability and optimal controls for fractional stochastic differential equations driven by Poisson...
  • S. Das, Functional Fractional Calculus. Springer-Verlag, Berlin, Heidelberg, 2011.
  • A. D. Fitt, A. R. H. Goodwin, K. A. Ronaldson and W. A. Wakeham, “A fractional differential equation for a MEMS viscometer used in the oil...
  • W. G. Glöckle and T. F. Nonnenmacher, “A fractional calculus approach of self-similar protein dynamics”, Biophysical Journal, vol. 68, no....
  • H. Aicha, J. J. Nieto and D. Amar, “Solvability and optimal controls of impulsive Hilfer fractional delay evolution inclusions with Clarke...
  • J. Wang, Y. Zhou, W. Wei and H. Xu, “Nonlocal problems for fractional integrodifferential equations via fractional operators and optimal controls”,...
  • E. J. Balder, “Necessary and sufficient conditions for L1-strong weak lower semicontinuity of integral functionals”, Nonlinear Analysis: Theory...
  • Y. Ren and R. Sakthivel, “Existence, uniqueness and stability of mild solutions for second-order neutral stochastic evolution equations with...
  • J. Dabas and A. Chauhan, “Existence and uniqueness of mild solution for an impulsive neutral fractional integro differential equations with...
  • K. Ramkumar, K. Ravikumar and S. Varshini, “Fractional neutral stochastic differential equations with Caputo fractional derivative: Fractional...