Abstract and Applied Analysis

Approximating the Solution of the Linear and Nonlinear Fuzzy Volterra Integrodifferential Equations Using Expansion Method

T. Allahviranloo, S. Abbasbandy, and S. Hashemzehi

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The present research study introduces an innovative method applying power series to solve numerically the linear and nonlinear fuzzy integrodifferential equation systems. Finally, it ends with some examples supporting the idea.

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Abstr. Appl. Anal., Volume 2014, Special Issue (2014), Article ID 713892, 7 pages.

First available in Project Euclid: 2 October 2014

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Allahviranloo, T.; Abbasbandy, S.; Hashemzehi, S. Approximating the Solution of the Linear and Nonlinear Fuzzy Volterra Integrodifferential Equations Using Expansion Method. Abstr. Appl. Anal. 2014, Special Issue (2014), Article ID 713892, 7 pages. doi:10.1155/2014/713892. https://projecteuclid.org/euclid.aaa/1412277360

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  • S. S. L. Chang and L. A. Zadeh, “On fuzzy mapping and control,” IEEE Transactions on Systems, Man, and Cybernetics, vol. 2, pp. 30–34, 1972.
  • L. A. Zadeh, “The concept of a linguistic variable and its application to approximate reasoning,” Information Sciences, vol. 8, no. 3, pp. 199–249, 1975.
  • M. Mizumoto and K. Tanaka, “The four operations of arithmetic on fuzzy numbers,” Systems Computers Controls, vol. 7, no. 5, pp. 73–81, 1976.
  • D. Dubois and H. Prade, “Operations on fuzzy numbers,” International Journal of Systems Science, vol. 9, no. 6, pp. 613–626, 1978.
  • S. Seikkala, “On the fuzzy initial value problem,” Fuzzy Sets and Systems, vol. 24, no. 3, pp. 319–330, 1987.
  • R. Goetschel Jr. and W. Voxman, “Elementary fuzzy calculus,” Fuzzy Sets and Systems, vol. 18, no. 1, pp. 31–43, 1986.
  • R. Alikhani, F. Bahrami, and A. Jabbari, “Existence of global solutions to nonlinear fuzzy Volterra integro-differential equations,” Nonlinear Analysis: Theory, Methods & Applications, vol. 75, no. 4, pp. 1810–1821, 2012.
  • T. Allahviranloo, M. Khezerloo, O. Sedaghatfar, and S. Salahshour, “Toward the existence and uniqueness of solutions of second-order fuzzy volterra integro-differential equations with fuzzy kernel,” Neural Computing and Applications, vol. 22, no. 1, pp. 133–141, 2013.
  • S. Hajighasemi, T. Allahviranloo, M. Khezerloo, M. Khorasany, and S. Salahshour, “Existence and uniqueness of solutions of fuzzy Volterra integro-differential equations,” in Information Processing and Management of Uncertainty in Knowledge-Based Systems, vol. 81 of Communications in Computer and Information Science, part 2, pp. 491–500, 2010.
  • B. Bede and L. Stefanini, “Generalized differentiability of fuzzy-valued functions,” Fuzzy Sets and Systems, vol. 230, pp. 119–141, 2013.
  • S. Salahshour and S. Abbasbandy, “A comment on “Global solutions for nonlinear fuzzy fractional integral and integrodifferential equations”,” Communications in Nonlinear Science and Numerical Simulation, vol. 19, no. 5, pp. 1256–1258, 2014.
  • T. Allahviranloo and S. Hashemzehi, “The homotopy perturbation method for fuzzy Fredholm integral equations,” Journal of Applied Mathematics, Islamic Azad University of Lahijan, vol. 19, pp. 1–13, 2008.
  • M. Gachpazan, “Numerical scheme to solve integro-differential equations system,” Journal of Advanced Research in Scientific Computing, vol. 1, no. 1, pp. 11–21, 2009.
  • B. Bede and S. G. Gal, “Generalizations of the differentiability of fuzzy-number-valued functions with applications to fuzzy differential equations,” Fuzzy Sets and Systems, vol. 151, no. 3, pp. 581–599, 2005.
  • L. A. Zadeh, “Fuzzy sets,” Information and Computation, vol. 8, pp. 338–353, 1965.
  • H. J. Zimmermann, Fuzzy Sets Theory and Its Applications, Kluwer, Dordrecht, The Netherlands, 1991.
  • D. Dubois and H. Prade, Fuzzy Sets and Systems, Academic Press, London, UK, 1980.
  • H. T. Nguyen, “A note on the extension principle for fuzzy sets,” Journal of Mathematical Analysis and Applications, vol. 64, no. 2, pp. 369–380, 1978.
  • M. L. Puri and D. A. Ralescu, “Fuzzy random variables,” Journal of Mathematical Analysis and Applications, vol. 114, no. 2, pp. 409–422, 1986.
  • M. Friedman, M. Ma, and A. Kandel, “Numerical solutions of fuzzy differential and integral equations,” Fuzzy Sets and Systems, vol. 106, no. 1, pp. 35–48, 1999.
  • Y. Chalco-Cano and H. Román-Flores, “On new solutions of fuzzy differential equations,” Chaos, Solitons and Fractals, vol. 38, no. 1, pp. 112–119, 2006.
  • T. Allahviranloo, N. Mikaeilvand, N. A. Kiani, and R. M. Shabestari, “Signed decomposition of fully fuzzy linear systems,” Applications and Applied Mathematics, vol. 3, no. 1, pp. 77–88, 2008. \endinput