Derivatives and integrals: matrix order operators as an extension of the fractional calculus

2020/04/30 by C.B. da Porciuncula, da Porciuncula, C. B.
Mathematics · Physics and Astronomy · #FOS: Mathematics #Fractional Differential Equations Solutions #General Mathematics (math.GM) #Mathematical functions and polynomials #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.2005.00091

openalex publication_date 2020/04/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A natural consequence of the fractional calculus is its extension to a matrix order of differentiation and integration. A matrix-order derivative definition and a matrix-order integration arise from the generalization of the gamma function applied to the fractional differintegration definition. This work focuses on some results applied to the Riemann-Liouville version of the fractional calculus extended to its matrix-order concept. This extension also may apply to other versions of fractional calculus. Some examples of possible ordinary and partial matrix-order differential equations and related exact solutions are shown.

Citations

• Matrix Order Differintegration
• Linear Models of Dissipation whose Q is almost Frequency Independent--II
• Fractional Differential Equations

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