DOI QR코드

DOI QR Code

IMPULSIVE FUZZY SOLUTIONS FOR ABSTRACT SECOND ORDER PARTIAL NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATIONS

  • CHALISHAJAR, DIMPLEKUMAR N. (Department of Applied Mathematics, Virginia Military Institute(VMI)) ;
  • RAMESH, R. (Department of Science and Humanities, Sri Krishna College of Engineering and Technology)
  • Received : 2021.10.13
  • Accepted : 2022.03.07
  • Published : 2022.03.30

Abstract

This work considers the existence and uniqueness of fuzzy solutions for impulsive abstract partial neutral functional differential systems. To establish the existence and uniqueness, we apply the concept of impulse, semi group theory and suitable fixed point theorem.

Keywords

References

  1. T. Allahviranloo and B. Ghanbari, On the fuzzy fractional differential equation with interval Atangana-Baleanu fractional derivative approach, Chaos, Solitons & Fractals 130 (2020), 93-97.
  2. D.N. Chalishajar and R. Ramesh, Fuzzy Solutions to Second Order Three Point Boundary Value Problem, Applications & Applied Mathematics 15 (2020), 916-927.
  3. E. Hernandez, Existence results for a partial second order functional differential equation with impulses, Dynamics of continuous discrete and impulsive systems series A 14 (2007), 229-250.
  4. O. Kaleva, The Cauchy problem for fuzzy differential equations, Fuzzy sets and systems 35 (1990), 389-396. https://doi.org/10.1016/0165-0114(90)90010-4
  5. A. Khastan, & R. Rodriguez-Lopez, An existence and uniqueness result for fuzzy Goursat partial differential equation, Fuzzy Sets and Systems 375 (2019), 141-160. https://doi.org/10.1016/j.fss.2019.02.011
  6. V. Lakshmikantham, & R.N. Mohapatra, Theory of fuzzy differential equations and inclusions, CRC press, 2004.
  7. H.V. Long, J.J. Nieto, & N. Son, New approach for studying nonlocal problems related to differential systems and partial differential equations in generalized fuzzy metric spaces, Fuzzy Sets and Systems 331 (2018), 26-46. https://doi.org/10.1016/j.fss.2016.11.008
  8. M. Mizumoto and J. Tanaka, Some properties of fuzzy numbers, M.M. Gupta et al., Eds., Advances in Fuzzy Set Theory and Applications (North-Holland, New York, 1979) 153-164.
  9. M. Puri, D. Ralescu, Fuzzy random variables, J. Math. Anal. Appl. 114 (1986), 409-422. https://doi.org/10.1016/0022-247X(86)90093-4
  10. R. Ramesh, & S. Vengataasalam, Existence and uniqueness theorem for a solution of fuzzy impulsive differential equations, Italian Journal of Pure and Applied Mathematics 33 (2014), 345-366.
  11. S. Tapaswini, S. Chakraverty, & T. Allahviranloo, A new approach to nth order fuzzy differential equations, Computational Mathematics and Modeling 28 (2017), 278-300. https://doi.org/10.1007/s10598-017-9364-3
  12. G. Wang, Y. Li, C. Wen, On fuzzy n-cell numbers and n-dimensional fuzzy vectors, Fuzzy sets and systems 158 (2007), 71-84. https://doi.org/10.1016/j.fss.2006.09.006