Some Results and Analysis of Nonlocal Special Random Impulsive Fractional Differential Equations

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Authors

  • Sayooj Aby Jose Ramanujan Centre for Higher Mathematics, Alagappa University, Karaikudi-630 004, India; Department of Mathematics, Alagappa University, Karaikudi-630 004, India Author
  • Ashitha Tom Department of Mathematics, Deva Matha College, Kuravilangad, Kerala Author
  • Juan Eduardo Napoles Valdes Department of Mathematics, UNNE-FACENA, Corrientes 3400, Argentina; Department of Mathematics, FRRE-UTN, Resistencia, Chaco, Argentina Author
  • Weerawat Sudsutad Theoretical and Applied Data Integration Innovations Group, Department of Statistics, Faculty of Science, Ramkhamhaeng University, Bangkok 10240, Thailand Author

DOI:

https://doi.org/10.5890/DNC.2023.06.006

Abstract

The aim of the paper is to present an analysis of special random impulsive fractional differential equations involving Fredholm and Volterra integrals. This paper is mainly focused to the existence, uniqueness and stability of special random impulsive fractional differential equations with local initial conditions and nonlocal initial conditions separately. Such an approach enabled the generalisation of equations with local initial conditions and also helps in obtaining more practical results. To test the effectiveness of our results, we provide examples.

References

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[5] Pleumpreedaporn, S., Sudsutad, W., Thaiprayoon, C., and Jose, S.A. (2021), Qualitative analysis of generalized proportional fractional functional integro-differential Langevin equation with variable coefficient and nonlocal integral conditions, Memoirs on Differential Equations and Mathematical Physics, 82, 1-22.

[6] Wu, S.J., Guo, X.L., and Lin, Z.S. (2006), Existence and uniqueness of solutions to random impulsive differential systems, Acta Mathematicae Applicatae Sinica, 4(2006), 627-632.

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[9] Anguraj, A., Wu, S.J., and Vinodkumar, A. (2011), The existence and exponential stability of semilinear functional differential equations with random impulses under non- uniqueness, Nonlinear Analysis, 74, 331-342.

[10] Yong, Z. and Wu, S.J. (2010), Existence and Uniqueness of solutions to stochastic differential equations with random impulsive under lipschitz conditions, Chinese Journal of Applied Probability and Statistics, 28, 347-356.

[11] Jose, S.A. and Usha, V. Existence and uniqueness of solutions for special random impulsive differential equation, Journal of Applied Science and Computations, 5(10), 14-23.

[12] Byszewski, L., and Lakshmikantham, V. (1990), Theorem about the existence and uniqueness of solutions of a nonlocal Cauchy problem in a Banach space, Applicable Analysis, 40(1990), 11-19.

[13] Jose, S.A., Yukunthorn, W., Valdes, J.E.N., and Leiva, H. (2020), Some Existence, Uniqueness and Stability Results of Nonlocal Random Impulsive Integro-Differential Equations, Applied Mathematics-E Notes, 20, 481-492

[14] Jose, S.A. and Usha, V. (2018), Existence of solutions for random impulsive differential equation with nonlocal conditions, International Journal of Computer Science and Engineering, 6(10), 549-554.

[15] Jose, S.A., Tom, A., Abinaya, S., and Yukunthorn, W. (2021), Some Characterization of Results of Nonlocal Special Random Impulsive Differential Evolution Equation, Journal of Applied Nonlinear Dynamics, 10(4), 711-723.

[16] Jose, S.A., Tom, A., Syed Ali, M., Abinaya, S., and Sudsutad, W. (2021), Existence, Uniqueness and Stability Results of Semilinear Functional Special Random Impulsive Differential Equations, Dynamics of Continuous, Discrete and Impulsive Systems Series A: Mathematical Analysis, 28, 269-293

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PublishedJune 2023

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How to Cite

Jose, S. A., Tom, A., Valdes, J. E. N., & Sudsutad, W. (2026). Some Results and Analysis of Nonlocal Special Random Impulsive Fractional Differential Equations. Discontinuity, Nonlinearity, and Complexity, 12(2), 299-312. https://doi.org/10.5890/DNC.2023.06.006