On the fractional counterpart of the higher-order equations

Abstract

In this work we study the solutions to some fractional higher-order equations. Special cases in which time-fractional derivatives take integer values are also examined and the explicit solutions are presented. Such solutions can be expressed by means of the transition laws of stable subordinators and their inverse processes. In particular we establish connections between fractional and higher-order equations.

References in corpus (7)

• Fractional Calculus: Integral and Differential Equations of Fractional Order
• The fundamental solution of the space-time fractional diffusion equation
• Fractional Cauchy problems on bounded domains
• Fractional diffusion equations and processes with randomly varying time
• Iterated Brownian motion in an open set
• Fokker-Planck-Kolmogorov equations associated with SDEs driven by time-changed fractional Brownian motion
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Cited by in corpus (8)

• Fractional equations via convergence of forms
• Coordinate changed random fields on manifolds
• Drifted Brownian motions governed by fractional tempered derivatives
• Studies on generalized Yule models
• Fractional Gamma process and fractional Gamma-subordinated processes
• Wright functions governed by fractional directional derivatives and fractional advection diffusion equations
• Time dependent random fields on spherical non-homogeneous surfaces
• Non-local logistic equations from the probability viewpoint