Caputo Fractional Operator on shallow water wave theory
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Keywords:
Fractional operator, singular kernel, numerical simulation, water wave, acousticsAbstract
In this section, we aim to introduce fractional operators that are applicable to real-world
scenarios, featuring both singular and nonsingular kernels. Given the extensive scope of fractional calculus,
which encompasses numerous mathematical and practical domains, we employ precise definitions
alongside shallow water wave theory models. This study offers numerical solutions for various wave theory
challenges, including wave height distribution across different depths, coastal engineering, and
electromagnetic wave phenomena. Numerical analysis and strategic approaches are crucial for obtaining
highly accurate estimates for barriers. The core of our numerical method lies in linearized wave equations,
focusing on variables such as particle velocity and surface elevation, derived from Eulerian motion and
continuity equations under the assumption of small amplitude in consistent water depth. We evaluate the
precision of discretization methods (e.g., finite difference or finite element techniques) based on step size
(h), noting that approaches where p > 2 often present higher error rates and are considered advanced.
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