Mathematics and Statistics Vol. 11(6), pp. 923 - 935
DOI: 10.13189/ms.2023.110607
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Adomian Decomposition Method for Solving Fuzzy Hilfer Fractional Differential Equations


V. Padmapriya 1,2, M. Kaliyappan 1,*
1 Division of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Chennai, India
2 New Prince Shri Bhavani Arts and Science College, Chennai, India

ABSTRACT

The field of fractional calculus is mainly concerned with the differentiation as well as integration of arbitrary orders. This concept is obviously present in various domains of science and engineering. Most people are familiar with the Caputo and Riemann-Liouville fractional definitions. Recently, Hilfer has related the Caputo and Riemann-Liouville derivatives by a general formula; this connection is referred to as the Hilfer or generalized Riemann-Liouville derivative. The Hilfer fractional derivative serves as an intermediary between the Riemann-Liouville and Caputo fractional derivatives, providing a means of interpolation. Parameters in the Hilfer derivative provide more degrees of freedom. Adomian decomposition method (ADM) is widely regarded as a highly effective mathematical technique for solving both linear and nonlinear differential equations. ADM provides an analytical solution in the form of a series solution. Motivated by the growing number of real-life applications for fractional calculus, the objective of this work is to explore the solutions of Hilfer fractional differential equations in a fuzzy sense using the ADM. The efficiency and accuracy of the proposed method are demonstrated by the solution of numerical examples. Graphical representations are provided to visualize the solutions' behavior. This shows that as the number of terms in the series goes up, the numerical results get closer and closer to the exact solutions.

KEYWORDS
Fuzzy Fractional Differential Equations, Riemann-Liouville Fractional Derivative, Caputo Fractional Derivative, Hilfer Fractional Derivative, Adomian Decomposition Method

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] V. Padmapriya , M. Kaliyappan , "Adomian Decomposition Method for Solving Fuzzy Hilfer Fractional Differential Equations," Mathematics and Statistics, Vol. 11, No. 6, pp. 923 - 935, 2023. DOI: 10.13189/ms.2023.110607.

(b). APA Format:
V. Padmapriya , M. Kaliyappan (2023). Adomian Decomposition Method for Solving Fuzzy Hilfer Fractional Differential Equations. Mathematics and Statistics, 11(6), 923 - 935. DOI: 10.13189/ms.2023.110607.