Solution of boundary value problem for fuzzy fractional differential equations by using differential transform method (DTM)

Authors

  • Mohammadreza Nourizadeh Germi Branch, Islamic Azad University
  • Rasol Mastani soffeyan Branch, Islamic Azad University

DOI:

https://doi.org/10.24200/jrset.vol3iss02pp8-11

Abstract

In this study, we implement a well-known transformation technique differential transform method (DTM), to the area of fractional differential equations, in this Paper, the solution to fuzzy fractional Initial Value Problem (FFIVP) under copout-type fuzzy fractional derivatives are define based on Hukuhara difference and strongly gene fuzzy differentiability. Also numerical examples are carried out for various types of problems including the Bagley-Torvik, Ricatti and composite fractional oscillation equations for the application of the method. 

References

T. Allahviranloo, S. Gholami, Note on Generalized Hukuhara differentiability of interval-value functions and interval differential equations, Journal of fuzzy set Valued Analysis, 2012. 4.

B .Bede, L. Stefanini, Generalizations differentiability of to fuzzy-valued functions, fuzzy Set and Systems, In press.

T. Allahviranloo, S. Salahshour, S. Abbasbandy, Explicit solutions of fractional differentia equations with auncertainty, Soft Comput. Fus. Found. Meth. Appl, 2012, 16 , 297-302.

T. Allahviranloo, S. Abbasbandy, S. Salahshour, Fuzzy fractional differential equations with Nagumo and Krasnoselskii-Krein condition, In: EUSFLAT-LFA 2011, july 2011, Aix-les-Bains, France.

Z. Odibat, S. Momani, Application of variational iteration method to nonlinear differential equations of fractional order, Int. J Nonlinear Sci. Numer. Simul. 2006, 1 (7) , 15-27.

B .Bede, S.G, Gal, Gneneralizations of the differentiability of fuzzy number valued functions with applications to fuzzy differential equations, fuzzy Set and Systems, 2005, 151 581-599.

C.K. Chen, S.H. Ho, Solving partial differential equations by two-dimensional differential transform method, Applied Mathematics and Computation, 1999, 106 ,171179.

M.J. Jang, C.L. Chen, Y.C. Liy, On solving the initial-value problems using the differential transformation method, Applied Mathematics and Computation , 2000, 115 ,145160.

A.Arikoglu, I. Ozkol, Solution of boundary value problems for integro-differential equations by using differential transform method, Appl. Math. Comput. 2005, 168 , 11451158.

Z. Odibat, N. Shawagfeh, Generalized Talyors formula, Appl. Math. Comput. 2007, 186 , 286293.

H. Liu, Y. Song, Differential transform method applied to high index differential-algebraic equations, Appl. Math. Comput. 2007,184 , 748753.

Podlubny, Fractional Differential Equations, Academic Press, NewYork, 1999.

Arikoglu A., Ozkol I. Solution of fractional differential equations by using differential transform method. Chaos Soliton Fract. doi:10.1016/j.chaos.2006.09.004.

Erturk VS, Momani S, Odibat Z. Application of generalized differential transform method to multi-order fractional differential equations. Commun Nonlinear Sci Numer Simul. doi:10.1016/j.cnsns.2007.02.006.

N. Bildik, A. Konuralp, F. Bek, S. Kucukarslan, Solution of different type of the partial differential equation by differential transform method and Adomians decomposition method, Appl. Math. Comput. 2006, 172 , 551567.

Published

2019-09-13

Issue

Section

Articles