Solution of Linear Fuzzy Fractional Differential Equations Using Fuzzy Natural Transform

  • Hameeda Oda Al-Humedi Department of Mathematics, College of Education for Pure Sciences, University of Basrah, Basrah, Iraq
  • Shaimaa Abdul-Hussein Kadhim Department of Mathematics, College of Education for Pure Sciences, University of Basrah, Basrah, Iraq
Keywords: Caputo’s H-difference, fuzzy fractional differential equations, fuzzy natural transform, Mittag-Leffler function


The purpose of this paper is to apply the fuzzy natural transform (FNT) for solving linear fuzzy fractional ordinary differential equations (FFODEs) involving fuzzy Caputo’s H-difference with Mittag-Leffler laws. It is followed by proposing new results on the property of FNT for fuzzy Caputo’s H-difference. An algorithm was then applied to find the solutions of linear FFODEs as fuzzy real functions. More specifically, we first obtained four forms of solutions when the FFODEs is of order α∈(0,1], then eight systems of solutions when the FFODEs is of order α∈(1,2] and finally, all of these solutions are plotted using MATLAB. In fact, the proposed approach is an effective and practical to solve a wide range of fractional models.


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How to Cite
Al-Humedi, H. O., & Kadhim, S. A.-H. (2021). Solution of Linear Fuzzy Fractional Differential Equations Using Fuzzy Natural Transform. Earthline Journal of Mathematical Sciences, 8(1), 41-65.