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Neural Computing and Applications

, Volume 22, Supplement 1, pp 133–141 | Cite as

Toward the existence and uniqueness of solutions of second-order fuzzy volterra integro-differential equations with fuzzy kernel

  • T. Allahviranloo
  • M. Khezerloo
  • O. Sedaghatfar
  • S. Salahshour
Original Article

Abstract

In this paper, we study existence and uniqueness of solutions of second-order fuzzy integro-differential equations with fuzzy kernel under strongly generalized differentiability. To this end, four cases are considered to show the existence of the fuzzy solution mentioned equation. Some theorems are proved, and the uniqueness of the fuzzy solution is discussed step by step. Finally, the illustrated examples are solved to investigate the conditions of theorems.

Keywords

Second-order fuzzy Volterra integro-differential equations Fuzzy valued functions Continuous solution 

Notes

Acknowledgments

The authors would like to present their sincere thanks to the Editor in Chief for his valuable suggestions.

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Copyright information

© Springer-Verlag London Limited 2012

Authors and Affiliations

  • T. Allahviranloo
    • 1
  • M. Khezerloo
    • 1
  • O. Sedaghatfar
    • 1
  • S. Salahshour
    • 2
  1. 1.Department of Mathematics, Science and Research BranchIslamic Azad UniversityTehranIran
  2. 2.Department of Mathematics, Mobarakeh BranchIslamic Azad UniversityMobarakehIran

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