Effective Approach to Construct Series Solutions for Uncertain Fractional Differential Equations
Purpose: We construct the analytical approximate resiual power fuzzy series solutions of fuzzy conformable fractional differential equations in an [Formula: see text]-level depiction in the sense of strongly generalized [Formula: see text]-fuzzy conformable derivative in which of the all initial con...
| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Tsinghua University Press
2022-04-01
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| Series: | Fuzzy Information and Engineering |
| Subjects: | |
| Online Access: | https://www.tandfonline.com/doi/10.1080/16168658.2022.2119041 |
| Summary: | Purpose: We construct the analytical approximate resiual power fuzzy series solutions of fuzzy conformable fractional differential equations in an [Formula: see text]-level depiction in the sense of strongly generalized [Formula: see text]-fuzzy conformable derivative in which of the all initial conditions are taken to be fuzzy numbers.Methodology: The certain fuzzy conformable fractional differential equation under strongly generalized [Formula: see text]-fuzzy derivative is converted to a crisp one as a family of differential inclusions and solved via resiual power method. The main drawback concerning the use of differential inclusions is that it does not contain a fuzzification of the differential operator; instead, the solution is not essentially a fuzzy valued function.Findings: (i) To show the efficiency of our proposed method: Several important and attractive test examples, which included the fractional conformable fuzzy integro-differential equation are discussed and solved in detail.(ii) To show the stability of approximate solutions to specific problems: some graphical results, numerical comparisons and tabulate data are created and discussed at different values ofValue: Using the residual power series analysis methos is a powerful and easy-to-use analytic tool to solve initial problems on fuzzy conformable fractional differential equations and it successfully applied to solve real life problems such as the inductance–resistance–capacitance, RLC-series circuit. |
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| ISSN: | 1616-8658 1616-8666 |