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arXiv · 2607.22659

Variational Formulations for Fractional Integral and Differential Equations

Delfim F. M. Torres
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Abstract

Given a fractional-order linear equation $L^\alpha u = f$, we define an appropriate symmetric bilinear form so that the fractional operator $L^\alpha$ is symmetric with respect to that bilinear form. Using the bilinear form, we then define a functional of the fractional calculus of variations proving that the solutions of the given fractional-order equation are critical points of the fractional variational functional. In the case of fractional integral equations, the provided bilinear form is non-degenerate, and all critical points are solutions of the given equation. In the case of fractional differential equations, a relation with the least-squares method is obtained.

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Delfim F. M. Torres. 2026-06-27. Variational Formulations for Fractional Integral and Differential Equations. https://arxiv.org/abs/2607.22659

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