LAUSR

ABSTRACT In this paper we investigate the solution of generalized distributed-order wave equations with composite time fractional derivative and external force, by using the Fourier–Laplace transform method. We represent the corresponding solutions in terms of infinite series in three parameter (Prabhakar), Mittag–Leffler and Fox H-functions, as well as in terms of the so-called Prabhakar integral operator. Generalized uniformly distributed-order wave equation is analysed by using the Tauberian theorem, and the mean square displacement is graphically represented by applying a numerical Laplace inversion algorithm. The numerical results and asymptotic behaviors are in good agreement. Some interesting examples of distributed-order wave equations with special external forces by using the Dirac delta function are also considered.