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

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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.

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Acknowledgments

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

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Authors and Affiliations

  1. Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran

    T. Allahviranloo, M. Khezerloo & O. Sedaghatfar

  2. Department of Mathematics, Mobarakeh Branch, Islamic Azad University, Mobarakeh, Iran

    S. Salahshour

Authors
  1. T. Allahviranloo
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  2. M. Khezerloo
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  3. O. Sedaghatfar
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  4. S. Salahshour
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Correspondence to T. Allahviranloo.

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Allahviranloo, T., Khezerloo, M., Sedaghatfar, O. et al. Toward the existence and uniqueness of solutions of second-order fuzzy volterra integro-differential equations with fuzzy kernel. Neural Comput & Applic 22 (Suppl 1), 133–141 (2013). https://doi.org/10.1007/s00521-012-0849-x

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  • DOI: https://doi.org/10.1007/s00521-012-0849-x

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