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Abstract

This paper deals with fuzzy Laplace transform to obtain the solution of fuzzy fractional differential equation (FFDEs) under Riemann Liouville H-differentiability .This is in contrast to conventional solution that either require a quantity of fractional derivative of unknown solution at the initial point(Riemann Liouville) or a solution with increasing length of their support (Hukuhara),using the fuzzy Laplace transform to solve differential equation with fractional order (0 < <1).The best of our knowledge,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.

References:-

References

Abbasbandy S, Shirzadi A. Homotopy analysis method for multiple solutions of the fractional Sturm–

Liouville problems. Numer Algor 2010;54:521–32.

Agarwal RP, Lakshmikantham V, Nieto JJ. On the concept of solution for fractional differential

equations with uncertainty. Nonlinear Anal 2010;72:2859–62.

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.

Arara A, Benchohra M, Hamidi N, Nieto JJ. Fractional order differential equations on an unbounded

domain. Nonlinear Anal 2010;72:580–6.

Lakshmikantham V, Vatsala AS. Basic theory of fractional differential equations. Nonlinear Anal

;69:2677–82.

Babenko YI. Heat and Mass Transfer, Chemia, Leningrad; 1986.

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.

Zimmermann HJ. Fuzzy set theory and its applications. Dordrecht: Kluwer Academi Publishers; 1991.

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

Kilbas AA, Srivastava HM, Trujillo JJ. Theory and applications of fractional differential equations.

Amesterdam: Elsevier Science B.V; 2006

Beyer H, Kempfle S. Definition of physically consistent damping laws with fractional derivatives.

ZAMM 1995;75:623–35.

Podlubny I. Fractional differential equation. San Diego: Academic Press; 1999.

Friedman M, Ma M, Kandel A. Numerical solution of fuzzy differential and integral equations. Fuzzy

Sets Syst 1999;106:35–48.

Ma M, Friedman M, Kandel A. Numerical solution of fuzzy differential equations. Fuzzy Sets Syst

;105:133–8.

wu Hc. The improper fuzzy Riemann integral and its numerical integration.Inform sci 1999;111:109-37

Allahviranloo T, Ahmadi MB. Fuzzy Laplace transforms. Soft Comput 2010;14:235–43.

Allahviranloo T,Salahshour S, Abbasbandy S. Explicit solutions of fractional differential equations with

uncertainty. Soft Comput. doi:10.1007/s00500-011-0743-y.

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Rubanraj, D. S., & Sangeetha, J. (2016). Fuzzy Laplace Transform With Fuzzy Fractional Differential Equation. International Journal Of Mathematics And Computer Research, 4(03), 1276-1282. Retrieved from http://ijmcr.in/index.php/ijmcr/article/view/30