Journal of Applied Science and Engineering

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Exact solutions of the conformable fractional differential systems with constant coefficients

 2026

 Volume 32

Yang Cai

Department of Mathematics, Pingxiang University, Pingxiang, China

Received: November 25, 2025
Accepted: March 30, 2026
Publication Date: May 27, 2026

上傳圖片

The current response i(t) for the same fractional orders 

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Conformable fractional calculus simplifies research and application due to its similarity with classical calculus in theory and operations. Therefore, it has gained significant attention from researchers and has accumulated rich theoretical achievements. The article establishes a comprehensive eigenvalue-based analytical system for constant coefficient flexible fractional differential systems by extending previous research work. The proposed method provides a systematic approach to eigenvalue classification, which results in four distinct eigenvalue categories and produces actual solutions for every category. The process of transforming complex eigenvalues into real solutions employs Euler’s formula, whereas the method for handling repeated roots uses a systematic approach of variable substitution. The framework establishes a complete theoretical foundation that describes high-dimensional conformable systems and demonstrates its validity through practical examples.

Keywords: Conformable Differential Systems, Constant Coefficients, Eigenvalue.

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