Fractional Calculus with Applications in Mechanics

This work explores fractional calculus and its applications in mechanics, particularly in viscoelasticity, heat conduction, and wave propagation, presenting rigorous mathematical analysis.

In Fractional Calculus with Applications in Mechanics, the authors delve into the foundational aspects of fractional calculus, introducing essential definitions and concepts related to fractional derivatives and their corresponding spaces. This mathematical groundwork sets the stage for exploring a variety of applications in classical mechanics, where the principles of fractional calculus are applied to complex phenomena such as viscoelasticity, heat conduction, wave propagation, and variational Hamilton-type principles. Each application is treated with mathematical rigor, ensuring that the theoretical underpinnings are clearly articulated.

The central section of the book is rich with practical applications, providing readers with a comprehensive understanding of how fractional calculus can be utilized in real-world scenarios. The authors present a series of problems that are formulated in both classical and distributional settings, offering a dual perspective on the challenges and solutions that arise in the field. Analytical solutions are provided for these problems, which are further analyzed through numerical methods, allowing for a deeper insight into the behavior of the systems under consideration.

Additionally, the book discusses theorems regarding the existence of solutions for all examples presented, along with the implications of the second law of thermodynamics in the context of various constitutive equations. The physical significance of the solutions obtained is examined in detail, making Fractional Calculus with Applications in Mechanics a valuable resource for both students and professionals seeking to understand the interplay between fractional calculus and mechanics.