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This research aims to establish the existence and uniqueness of solutions for multi-order Caputo fractional differential equations.

June 2, 2026Open Access

Solving Multi-order Nonlinear Caputo Fractional Differential Equations and Numerical Simulations

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This research aims to establish the existence and uniqueness of solutions for multi-order Caputo fractional differential equations.
Utilized Banach contraction principle to derive sufficient conditions for solutions.
Implemented a modified Adams-Bashforth-Moulton predictor-corrector method for numerical simulations.
Presented three illustrative examples to verify theoretical findings.
Demonstrated existence and uniqueness of solutions under established conditions.
Showed significant impact of fractional orders on coupled oscillators and memory effects on dynamics.
Confirmed robustness of proposed methods through numerical case studies.

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Randomized trial investigates solution uniqueness in multi-order fractional systems, indicating practical methods exist.

Abdalla et al. (2025) studied this question.

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