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Journal of Mathematics, Physics and Mechanics

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Analytical Solutions of Fractional Differential Equations: A Case Study Using MathHandbook
Case Study - Volume: 1, Issue: 1, 2026 (September)
Analytical Solutions of Fractional Differential Equations: A Case Study Using MathHandbook Download PDF
Weiguang Huang* ORCID

Department of Chemistry, University of New South Wales, Syndey, Australia
*Correspondence to: Weiguang Huang, Department of Chemistry, University of New South Wales, Syndey, Australia, E-Mail:
Received: August 13, 2026; Manuscript No: JMPM-26-6203; Editor Assigned: August 15, 2026; PreQc No: JMPM-26-6203(PQ); Reviewed: August 20, 2026; Revised: August 25, 2026; Manuscript No: JMPM-26-6203(R); Published: September 07, 2026

ABSTRACT

This study investigates analytical solutions of fractional differential equations (FDEs) using the MathHandbook symbolic computation platform. The objective is to evaluate how the unified operator ds (y,x,α) and the dsolve engine handle differential equations of arbitrary order, including integer-order ODEs/PDEs, fractional ODEs and PDEs, fractional integral equations, mixed differential–integral equations, systems of fractional equations, complex-order equations, and variable-order equations. Comparative analysis shows that general solutions exhibit order-dependent exponential behavior, while particular solutions remain invariant for linear equations with identical forcing terms. These results highlight the coherence of fractional calculus and demonstrate how AI-Driven symbolic computation enhances mathematical modeling, verification, and mathematics education.

Keywords: Fractional Differential Equations; Fractional Calculus; Symbolic Computation; Mathhandbook; Analytical Solutions; Differential Equations; Fractional-Order Derivatives; Variable-Order Equations; Complex-Order Equations; AI-Driven Mathematics

Citation: Huang W (2026). Analytical Solutions of Fractional Differential Equations: A Case Study Using MathHandbook. J. Math. Phys. Mech. Vol.1 Iss.1, September (2026), pp:1-7.
Copyright: © 2026 Weiguang Huang. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.