Granular fractional Caputo-Katugampola derivatives and their applications in optimality conditions for fuzzy fractional variational problems

Le Thanh Tung; Tran Thien Khai; Pham Le Bach Ngoc; Trinh Tung

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arXiv · 2607.22559

Granular fractional Caputo-Katugampola derivatives and their applications in optimality conditions for fuzzy fractional variational problems

Le Thanh Tung·Tran Thien Khai·Pham Le Bach Ngoc·Trinh Tung

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Abstract

In this article, we present the new definition of the fuzzy Caputo-Katugampola derivative and its related concepts for the class of fuzzy functions and apply them to establish both necessary and sufficient optimality conditions for fractional fuzzy variational problems. By adopting the horizontal membership functional representation of fuzzy numbers, the granular Caputo-Katugampola derivatives offer higher computational efficiency than the previous approaches in certain scenarios. The optimality conditions for the fuzzy fractional variational problems under granular fuzzy Caputo fractional derivatives are also examined and illustrated with detailed examples. Another novel aspect of our results, even in the non-fuzzy case, is the application of special functions to represent the exact solutions of the fuzzy fractional variational problems.

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Le Thanh Tung, Tran Thien Khai, Pham Le Bach Ngoc, Trinh Tung. 2026-05-28. Granular fractional Caputo-Katugampola derivatives and their applications in optimality conditions for fuzzy fractional variational problems. https://arxiv.org/abs/2607.22559

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