What question did this study set out to answer?

This research aims to establish the existence and uniqueness of solutions for nonlinear Volterra integral equations with variable fractional order.

Existence and Uniqueness of Nonlinear Volterra Integral Equations With Variable Fractional Order in Fréchet Spaces via a Frigon−Granas Fixed Point Approach

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Investigation finds solutions to nonlinear Volterra integral equations in Fréchet spaces, suggesting new approaches in fractional calculus.

This research aims to establish the existence and uniqueness of solutions for nonlinear Volterra integral equations with variable fractional order.
Examined Volterra integral equations in Fréchet spaces.
Utilized the Riemann–Liouville fractional derivative.
Applied the Frigon–Granas fixed-point theorem.
Considered problems on semi-infinite intervals.
Demonstrated existence of solutions under general conditions.
Showed uniqueness of solutions for the specified equations.
Provided illustrative examples validating the main results.

Telli et al. (2026) studied this question.

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Investigation finds solutions to nonlinear Volterra integral equations in Fréchet spaces, suggesting new approaches in fractional calculus.