Solving Fuzzy Fractional Differential Equation with Fuzzy Laplace Transform Involving Sine function

Dr.S. Rubanraj; J. sangeetha

doi:https://doi.org/10.14445/22315373/IJMTT-V48P531

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 48 | Number 4 | Year 2017 | Article Id. IJMTT-V48P531 | DOI : https://doi.org/10.14445/22315373/IJMTT-V48P531

Solving Fuzzy Fractional Differential Equation with Fuzzy Laplace Transform Involving Sine function

Dr.S. Rubanraj, J. sangeetha

Abstract

This paper deals with fuzzy Laplace transforms to obtain the solution of fuzzy fractional differential equation (FFDEs) under Riemann Liouville H-differentiability with fractional order (0 < <1). There is limited research devoted to the analytical method to solve the FFDEs under Riemann Liouville Hdifferentiability. An analytical solution is presented to confirm the capability of proposed method.

Keywords

An analytical solution is presented to confirm the capability of proposed method.

References

[1] Abbasbandy S, Shirzadi A. Homotopy analysis method for multiple solutions of the fractional Sturm–Liouville problems. Numer Algor 2010;54:521–32.
[2] Agarwal RP, Lakshmikantham V, Nieto JJ. On the concept of solution for fractional differential equations with uncertainty. Nonlinear Anal 2010;72:2859–62.
[3] Allahviranloo T, Salahshour S. A new approach for solving first order fuzzy differential equations. Commun Comput Inform Sci 2010;81:522–31. Part 5Part 7.
[4] Arara A, Benchohra M, Hamidi N, Nieto JJ. Fractional order differential equations on an unbounded domain. Nonlinear Anal 2010;72:580–6.
[5] Lakshmikantham V, Vatsala AS. Basic theory of fractional differential equations. Nonlinear Anal 2008;69:2677–82.
[6] Babenko YI. Heat and Mass Transfer, Chemia, Leningrad; 1986.
[7] Bede B, Gal SG. Generalizations of the differentiability of fuzzy-number-valued functions with applications to fuzzy differential equations. Fuzzy Sets Syst 2005;151:581–99.
[8] Zimmermann HJ. Fuzzy set theory and its applications. Dordrecht: Kluwer Academi Publishers; 1991.
[9] Dr. S. Rubanraj , J. Sangeetha Fuzzy Laplace Transform With Fuzzy Fractional Differential Equation volume4 ijmcr -p.1276-82
[10] Kilbas AA, Srivastava HM, Trujillo JJ. Theory and applications of fractional differential equations. Amesterdam: Elsevier Science B.V; 2006
[11] Beyer H, Kempfle S. Definition of physically consistent damping laws with fractional derivatives. ZAMM 1995;75:623–35.
[12] Podlubny I. Fractional differential equation. San Diego: Academic Press; 1999.
[13] Friedman M, Ma M, Kandel A. Numerical solution of fuzzy differential and integral equations. Fuzzy Sets Syst 1999;106:35–48.
[14] Ma M, Friedman M, Kandel A. Numerical solution of fuzzy differential equations. Fuzzy Sets Syst 1999;105:133–8.
[15]wu Hc. The improper fuzzy Riemann integral and its numerical integration.Inform sci 1999;111:109-37
[16] Allahviranloo T, Ahmadi MB. Fuzzy Laplace transforms. Soft Comput 2010;14:235–43.
[17]Allahviranloo T,Salahshour S, Abbasbandy S. Explicit solutions of fractional differential equations with uncertainty. Soft Comput. doi:10.1007/s00500-011-0743-y.
[18] Bagley RL On the fractional order initial value problem and its engineering applications. In: Nishimoto K, editor. Fractional calculus and its applications. Tokyo: College of Engineering, Nihon University;1990. p. 12–20.

Citation :

Dr.S. Rubanraj, J. sangeetha, "Solving Fuzzy Fractional Differential Equation with Fuzzy Laplace Transform Involving Sine function," International Journal of Mathematics Trends and Technology (IJMTT), vol. 48, no. 4, pp. 218-222, 2017. Crossref, https://doi.org/10.14445/22315373/IJMTT-V48P531