Journal
COMPUTATIONAL & APPLIED MATHEMATICS
Volume 40, Issue 3, Pages -Publisher
SPRINGER HEIDELBERG
DOI: 10.1007/s40314-021-01476-9
Keywords
Fuzzy differential equations of integer and non-integer order derivatives; Fuzzy Shehu transform method; Caputo gH-derivative; Homotopy analysis transform algorithm; Numeric-symbolic computation
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Funding
- National Natural Science Foundations of China [11571206, 12071261, 12001539, 11831010, 11871068]
- Science Challenge Project [TZ2018001]
- National Key Basic Research Program [2018YFA0703903]
- China Scholarship Council (CSC) [2017GXZ025381]
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The paper introduces a new fuzzy Shehu transform method using Zadeh's decomposition theorem and fuzzy Riemann integral on finite intervals. By combining this method with the homotopy analysis method, it provides effective solutions for fuzzy differential equations of integer and non-integer order derivatives, supported by convergence analysis and error analysis. Numerical simulations of exact and approximate solutions further demonstrate the reliability and efficiency of the proposed method.
In this paper, we propose the fuzzy Shehu transform method (FSTM) using Zadeh's decomposition theorem and fuzzy Riemann integral of real-valued functions on finite intervals. As an alternative to standard fuzzy Laplace transform and the fuzzy Sumudu integral transform, we established some potential useful (new or known) properties of the FSTM and validate their applications. Furthermore, the FSTM is coupled with the well-known homotopy analysis method to obtain the approximate and exact solutions of fuzzy differential equations of integer and non-integer order derivatives. The convergence analysis and the error analysis of the suggested technique are provided and supported by graphical solutions. Comparison of the numerical simulations of exact and approximate solutions of two fuzzy fractional partial differential equations are tabulated to further justify the reliability and efficiency of the proposed method.
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