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International Journal of Creative and Open Research in Engineering and Management

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ISSN: 3108-1754 (Online)
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Peer Review: Double Blind
Volume 02, Issue 10

Published on: October 2026

STRUCTURAL INVALIDITY OF THE MODIFIED CHAIN RULE IN HE ET AL.

Weiguang Huang

DrHuang.com, Sydney, NSW 2033, Australia
DOI:https://doi.org/10.55041/ijcope.v2i10.123

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Abstract

This work re-examines the modified chain-rule identity proposed by He, Elagan, and Li (2012). Although they correctly demonstrate that the previously used chain rule is invalid, the replacement formula containing a geometric scaling factor does not resolve the underlying analytic inconsistency. Both identities share the same local-product structure, which is incompatible with the integral definition of Jumarie’s modified Riemann–Liouville derivative. Multiple counterexamples show that no fixed geometric constant can make the modified identity valid. Consequently, the reduction procedure in Section 5 of the original paper lacks mathematical justification, and subsequent works relying on this chain rule should be revisited. This clarification helps prevent further propagation of incorrect chain-rule assumptions in fractional-calculus research.

Keywords: Chain rule, Jumarie, Riemann–Liouville derivative, fractional calculus, fractional complex transform.

How to Cite this Paper

Huang, W. (2026). Structural Invalidity of the Modified Chain Rule in He et al.. International Journal of Creative and Open Research in Engineering and Management, <i>02</i>(10), 1-9. https://doi.org/10.55041/ijcope.v2i10.123

Huang, Weiguang. "Structural Invalidity of the Modified Chain Rule in He et al.." International Journal of Creative and Open Research in Engineering and Management, vol. 02, no. 10, 2026, pp. 1-9. doi:https://doi.org/10.55041/ijcope.v2i10.123.

Huang, Weiguang. "Structural Invalidity of the Modified Chain Rule in He et al.." International Journal of Creative and Open Research in Engineering and Management 02, no. 10 (2026): 1-9. https://doi.org/https://doi.org/10.55041/ijcope.v2i10.123.

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References


  1. Huang, (2026). J. Software Engineering and Simulation, 12(2): 46–51. https://www.questjournals.org/jses/papers/Vol12-issue-2/12024651.pdf

  2. Huang, (2026). Int. J. Creative and Open Research in Engineering and Management, 2(10), 1-9. https://doi.org/10.55041/ijcope.v2i10.039

  3. Jumarie, Modified Riemann–Liouville derivative and fractional Taylor series of nondifferentiable functions: further results, Comput. Math. Appl. 51 (2006) 1367–1376.

  4. B. Li, An extended fractional complex transform, Int. J. Nonlinear Sci. Numer. Simul. 11 (2010) 335–337.

  5. B. Li and J.H. He, Application of the fractional complex transform to fractional differential equations, Nonlinear Sci. Lett. A 2 (2011) 121–126.

  6. H. He, A short remark on fractional variational iteration method, Phys. Lett. A 375 (2011) 3362–3364.

  7. Yinghui He, Weiguo Rui, “Extended Separation Method of Semi-Fixed Variables Together With Analytical Method for Solving Time Fractional Equation,” Methods in the Applied Sciences, 48 (2025), 9934–9945.

  8. Zheng-Biao Li, Ji-Huan He, “Fractional Complex Transform for Fractional Differential Equations,” and Computational App., 15 (2010), 970–973.

  9. Ji-Huan He, “A Tutorial Review on Fractal Spacetime and Fractional Calculus,” International Journal of Theoretical Physics, 53 (2014), 3698–3718.

  10. Ji-Huan He, Zheng-Biao Li, “Converting Fractional Differential Equations into Partial Differential Equations,” Thermal Science, 16 (2012), 331–334.

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  • •Published on: Oct 20 2026
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