The paper by Igor Podlubny addresses the long-standing problem of geometric and physical interpretations of fractional integration and differentiation. It proposes a new approach to interpreting these operations, particularly for Riemann-Liouville fractional integration, Caputo fractional differentiation, Riesz potential, and Feller potential. The author also generalizes these interpretations to more general convolution integrals of the Volterra type and provides a new physical interpretation for the Stieltjes integral. The geometric interpretation of fractional integration is based on the concept of a "fence" that varies in shape as time progresses, with its shadows on different planes representing the integral values. This interpretation is extended to fractional differentiation, where the relationship between individual and cosmic time is described by a function. The physical interpretation of fractional integration is linked to the idea of inhomogeneous time scales, where the cosmic time flows non-uniformly, affecting the calculation of real distances and velocities. The paper also discusses the use of two types of time—cosmic time and individual time—and how these interpretations align with current physical theories, such as the expansion of the universe and the concept of dynamic time scales. Finally, the geometric and physical interpretations are extended to convolution integrals, providing a comprehensive framework for understanding fractional calculus in both theoretical and applied contexts.The paper by Igor Podlubny addresses the long-standing problem of geometric and physical interpretations of fractional integration and differentiation. It proposes a new approach to interpreting these operations, particularly for Riemann-Liouville fractional integration, Caputo fractional differentiation, Riesz potential, and Feller potential. The author also generalizes these interpretations to more general convolution integrals of the Volterra type and provides a new physical interpretation for the Stieltjes integral. The geometric interpretation of fractional integration is based on the concept of a "fence" that varies in shape as time progresses, with its shadows on different planes representing the integral values. This interpretation is extended to fractional differentiation, where the relationship between individual and cosmic time is described by a function. The physical interpretation of fractional integration is linked to the idea of inhomogeneous time scales, where the cosmic time flows non-uniformly, affecting the calculation of real distances and velocities. The paper also discusses the use of two types of time—cosmic time and individual time—and how these interpretations align with current physical theories, such as the expansion of the universe and the concept of dynamic time scales. Finally, the geometric and physical interpretations are extended to convolution integrals, providing a comprehensive framework for understanding fractional calculus in both theoretical and applied contexts.