Abstract
In this paper, we will investigate existence and uniqueness of solutions of fuzzy Volterra integrro-differential equations of the second kind with fuzzy kernel under strongly generalized differentiability. To this end, some new results are derived for Hausdorff metric.
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References
Allahviranloo, T., Kiani, N.A., Barkhordari, M.: Toward the existence and uniqueness of solutions of second-order fuzzy differential equations. Information Sciences 179, 1207–1215 (2009)
Bede, B., Rudas, I.J., Attila, L.: First order linear fuzzy differential equations under generalized differentiability. Information Sciences 177, 3627–3635 (2007)
Bede, B., Gal, S.G., Generalizations of the differentiability of fuzzy-number-valued functions with applications to fuzzy differential equations. Fuzzy Sets and Systems 151, 581–599 (2005)
Chalco-cano, Y., Roman-Flores, H.: On new solution of fuzzy differential equations. Chaos, Solitons and Fractals 38, 112–119 (2008)
Dubois, D., Prade, H.: Towards fuzzy differential calculus, Part I: integration of fuzzy mappings, class of second-order. Fuzzy sets and Systems 8, 1–17 (1982)
Friedman, M., Ma, M., Kandel, A.: Numerical solution of fuzzy differential and integral equations. Fuzzy Sets and System 106, 35–48 (1999)
Kaleva, O.: The Cauchy problem for fuzzy differential equations. Fuzzy sets and Systems 35, 389–396 (1990)
Park, J.Y., Jeong, J.U.: A note on fuzzy functional equations. Fuzzy Sets and Systems 108, 193–200 (1999)
Park, J.Y., Kwun, Y.C., Jeong, J.U.: Existence of solutions of fuzzy integral equations in Banach spaces. Fuzzy Sets and Systems 72, 373–378 (1995)
Park, J.Y., Lee, S.Y., Jeong, J.U.: On the existence and uniqueness of solutions of fuzzy Volterra-Fredholm integral equuations. Fuzzy Sets and Systems 115, 425–431 (2000)
Puri, M.L., Ralescu, D.A.: Differentials of fuzzy functions. J. Math. Anal. Appl. 91, 552–558 (1983)
Rodriguez-Munize, L.J., Lopez-Diaz, M.: Hukuhara derivative of the fuzzy expected value. Fuzzy Sets and Systems 138, 593–600 (2003)
Rodriguez-Lipez, R.: Comparison results for fuzzy differential equations. Information Sciences 178, 1756–1779 (2008)
Seikkala, S.: On the fuzzy initial value problem. Fuzzy Sets and Systems 24, 319–330 (1987)
Stefanini, L.: On the generalized LU-fuzzy derivative and fuzzy differential equations. In: IEEE International Conference on Fuzzy Systems, art. no. 4295453 (2007)
Subrahmaniam, P.V., Sudarsanam, S.K.: On some fuzzy functional equations. Fuzzy Sets and Systems 64, 333–338 (1994)
Zhang, D., Feng, W., Qiu, J.: Global existence of solutions to fuzzy Volterra integral equations. ICIC Express Letters 3, 707–711 (2009)
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Hajighasemi, S., Allahviranloo, T., Khezerloo, M., Khorasany, M., Salahshour, S. (2010). Existence and Uniqueness of Solutions of Fuzzy Volterra Integro-differential Equations. In: Hüllermeier, E., Kruse, R., Hoffmann, F. (eds) Information Processing and Management of Uncertainty in Knowledge-Based Systems. Applications. IPMU 2010. Communications in Computer and Information Science, vol 81. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14058-7_51
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DOI: https://doi.org/10.1007/978-3-642-14058-7_51
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