# Fuzzy generalized fractional power series technique for simulating fuzzy fractional relaxation problem

## Abstract

In this paper, the fuzzy generalized fractional power series method is proposed to obtain the numerical solutions of a class of fuzzy fractional relaxation problems. For this purpose, the fuzzy generalized fractional power series under different types of the Caputo generalized Hukuhara differentiability are introduced. Some theorems are generalized for the fuzzy generalized fractional power series. This method is based on first taking the truncated fuzzy generalized fractional power series of the functions in the relaxation problem and then substituting them into the equation. Hence, the result equation can be solved, and the unknown fuzzy coefficients can be found. In addition, to demonstrate the efficiency of the method, some examples are solved.

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## Data Availability

Enquiries about data availability should be directed to the authors.

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## Acknowledgements

The authors would like to express deep gratitude to the editors and referees for their valuable suggestions which led us to a better presentation of this paper.

## Funding

No funding was received to assist with the preparation of this manuscript.

## Author information

Authors

### Contributions

KE conceived of the presented idea. TA developed the theory and contributed to the design and implementation of the research. MR-M and MHB contributed to the analysis of the results and the writing of the manuscript. TA supervised the project. All authors discussed the results and contributed to the final manuscript.

### Corresponding author

Correspondence to Tofigh Allahviranloo.

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Ebdalifar, K., Allahviranloo, T., Rostamy-Malkhalifeh, M. et al. Fuzzy generalized fractional power series technique for simulating fuzzy fractional relaxation problem. Soft Comput 27, 2171–2184 (2023). https://doi.org/10.1007/s00500-022-07742-0

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• DOI: https://doi.org/10.1007/s00500-022-07742-0

### Keywords

• Caputo generalized Hukuhara differentiability
• Fuzzy generalized fractional power series method
• Fuzzy fractional relaxation problems
• Fuzzy triangular numbers