Fuzzy Sumudu Transforms of the Fuzzy Riemann-Liouville Fractional Derivatives About Order


  • Roaa Hameed Hassan
  • Yasir Mohammad Abbas
  • . .






Fuzzy sumudu transform, fuzzy Riemann-Liouville fractional derivatives, Mittag-leffeler. Mathematic applied/MSc 2015.


This work involved fuzyy Sumudu transform (FST) for solving fuzzy fractional differential equations (FFDEs) involving Riemann-Liouvillefuzzy fractional derivative and we find with proof the formulas of fuzzy sumudu transforms for Riemann-Liouville fuzzy fractional derivative about order . Addition, we use the resulting fuzzy Sumudu transform to solve (FFDEs) of order .




[1] Rahman NAA & Ahmad MZ, “Applications of the fuzzy Sumudu transform for the solution of first order fuzzy differential equationsâ€, Entropy, Vol.17, No.7, (2015), pp.4582-4601.

[2] Rahman NAA & Ahmad MZ, “Solving fuzzy fractional differential equations using fuzzy Sumudu transformâ€, Journal of Nonlinear Science and Applications, Vol.201, (2017), pp.1-15.

[3] Agrawal OP, “Solution for a fractional diffusion-wave equation defined in a bounded domainâ€, Nonlinear Dynamics, Vol.29, No.1-4, (2002), pp.145-155.

[4] Ahmad MZ & Bin Abdul Rahman NA, “Explicit solution of fuzzy differential equations by mean of fuzzy Sumudu transformâ€, International Journal of Applied Physics and Mathematics, Vol.5, No.2, (2015), pp.86-93.

[5] Allahviranloo T & Ahmadi MB, “Fuzzy laplace transformsâ€, Soft Computing, Vol.14, No.3, (2010), pp.235–243.

[6] Benson DA, Wheatcraft SW & Meerschaert MM, “Application of a fractional advectionâ€dispersion equationâ€, Water resources research, Vol.36, No.6, (2000), pp.1403-1412.

[7] Bhrawy AH & Zaky MA, “Shifted fractional-order Jacobi orthogonal functions: application to a system of fractional differential equationsâ€, Applied Mathematical Modelling, Vol.40, No.2, (2016), pp.832-845.

[8] Bulut F, Oruç Ö & Esen A, “Numerical solutions of fractional system of partial differential equations by Haar waveletsâ€, Computer Modeling in Engineering & Sciences, Vol.108, No.4, (2015), pp.263-284.

[9] Garg V & Singh K, “An improved Grunwald-Letnikov fractional differential mask for image texture enhancementâ€, International Journal of Advanced Computer Science and Applications, Vol.3, No.3, (2012), pp.130-135.

[10] Glöckle WG & Nonnenmacher TF, “A fractional calculus approach to self-similar protein dynamicsâ€, Biophysical Journal, Vol.68, No.1, (1995), pp.46-53.

[11] Haydar AK, “Fuzzy Sumudu transform for fuzzy nth-order derivative and solving fuzzy ordinary differential equationsâ€, Int. J. Sci. Res., Vol. 4, (2015), pp.1372-1378.

[12] Jarad F & TaÅŸ K, “Application of Sumudu and double Sumudu transforms to Caputo-Fractional differential equationsâ€, J. Comput. Anal. Appl., Vol.14, (2012), pp.475–483.

[13] Jumarie G, “Fractional partial differential equations and modified Riemann-Liouville derivative new methods for solutionâ€, Journal of Applied Mathematics and Computing, Vol.24, No.1-2, (2007), pp.31-48.

[14] AKilbas AA & Marzan SA, “Nonlinear differential equations with the Caputo fractional derivative in the space of continuously differentiable functionsâ€, Differential Equations, Vol.41, No.1, (2005), pp.84-89.

[15] Kilbas AA, Srivastava HM & Trujillo JJ, Theory and applications of fractional differential equations, North-Holland Mathematics Studies, Elsevier Science B.V., Amsterdam, (2006).

[16] Layman JW, “The Hankel transform and some of its propertiesâ€, J. Integer Seq., Vol.4, No.1, (2001), pp.1-11.

[17] Lupulescu V, “Fractional calculus for interval-valued functionsâ€, Fuzzy sets and systems, Vol.265, (2015), pp.63-85.

[18] Mazandarani M & Kamyad AV, “Modified fractional Euler method for solving fuzzy fractional initial value problemâ€, Communications in Nonlinear Science and Numerical Simulation, Vol.18, No.1, (2013), pp.12-21.

[19] Podlubny I, Fractional differential equations, An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications, Mathematics in Science and Engineering, Academic Press, Inc., San Diego, CA, (1999).

[20] Podlubny I, Fractional Differential Equations, Mathematics in Science and Engineering, Academic Press USA, (1999).

[21] Salahshour S, Allahviranloo T & Abbasbandy S, “Solving fuzzy fractional differential equations by fuzzy Laplace transformsâ€, Communications in Nonlinear Science and Numerical Simulation, Vol.17, No.3, (2012), pp.1372-1381.

[22] Sousa E & Li C, “A weighted finite difference method for the fractional diffusion equation based on the Riemann–Liouville derivativeâ€, Applied Numerical Mathematics, Vol.90, (2015), pp.22-37.

[23] Spinelli RA, “Numerical inversion of a Laplace transformâ€, SIAM Journal on Numerical Analysis, Vol.3, No.4, (1966), pp.636-649.

[24] Tranter CJ, “The use of the Mellin transform in finding the stress distribution in an infinite wedgeâ€, The Quarterly Journal of Mechanics and Applied Mathematics, Vol.1, No.1, (1948), pp.125-130.

[25] Watugala GK, “Sumudu transform: a new integral transform to solve differential equations and control engineering problemsâ€, Integrated Education, Vol.24, No.1, (1993), pp.35-43.

[26] Wu HC, “The improper fuzzy Riemann integral and its numerical integrationâ€, Information Sciences, Vol.111, No.1-4, (1998), pp.109-137.

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How to Cite

Hameed Hassan, R., Mohammad Abbas, Y., & ., . (2018). Fuzzy Sumudu Transforms of the Fuzzy Riemann-Liouville Fractional Derivatives About Order. International Journal of Engineering & Technology, 7(4.25), 363–367. https://doi.org/10.14419/ijet.v7i4.25.27015
Received 2019-02-02
Accepted 2019-02-02
Published 2018-11-30