Analytical solutions of fractional wave equation with memory effect using the fractional derivative with exponential kernel
B. Cuahutenango-Barro, M.A. Taneco-Hernández, Yu-Pei Lv, J. F. Gómez‐Aguilar, M.S. Osman, Hadi Jahanshahi, Ayman A. Aly
Abstract
Analytical solutions of the fractional wave equation via Caputo-Fabrizio fractional derivative are presented in this paper. For this analysis, three cases are considered, the classical, the damped and the damped with a source term defined by fractional wave equations. We show that these solutions are special cases of the time fractional equations with exponential law. Illustrative examples are presented.
Topics & Concepts
Fractional calculusExponential functionMathematicsDerivative (finance)Wave equationMathematical analysisKernel (algebra)Applied mathematicsMittag-Leffler functionPhysicsPure mathematicsFinancial economicsEconomicsFractional Differential Equations SolutionsNonlinear Waves and SolitonsNumerical methods in engineering