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Multi-term Time-Fractional Stochastic Differential Equations with Non-Lipschitz Coefficients

  • Vikram SinghEmail author
  • Dwijendra N Pandey
Original Research
  • 3 Downloads

Abstract

In this paper, we study the existence and uniqueness of mild solutions for a class of multi-term time-fractional stochastic differential equations in Hilbert spaces. We tend to implement fractional calculus, generalized semigroup theory and stochastic analysis techniques to obtain the main results. We come up with a new set of sufficient conditions with the coefficients in the equations satisfying some non-Lipschitz conditions and using standard Picard type iterations. Finally, an application is given to illustrate that our obtained results are valuable.

Keywords

Fractional calculus Generalized semigroup theory Multi-term time-fractional stochastic differential equations Mild solution Non-Lipschitz coefficient 

Mathematics Subject Classification

34A08 34G20 26A33 34A12 65C30 47H10 

Notes

Acknowledgements

The work of the first author is supported by the “Ministry of Human Resource and Development, India under Grant number: MHR-02-23-200-44”.

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Copyright information

© Foundation for Scientific Research and Technological Innovation 2019

Authors and Affiliations

  1. 1.Department of MathematicsIndian Institute of Technology RoorkeeRoorkeeIndia

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