Differential Equations of Fractional Order: Methods, Results and Problems. II

The article, being a continuation of the first one [A.A. Kilbas and J.J. Trujillo (2001). Differential equations of fractional order. Methods, results and problems, I. Applicable Analysis , 78 (1-2), 153-192.], deals with the so-called differential equations of fractional order in which an unknown function is contained under the operation of a derivative of fractional order. The methods and the results in the theory of such fractional differential equations are presented including the Dirichlet-type problem for ordinary fractional differential equations, studying such equations in spaces of generalized functions, partial fractional differential equations and more general abstract equations, and treatment of numerical methods for ordinary and partial fractional differential equations. Problems and new trends of research are discussed.

Keywords:

• Fractional Calculus
• Ordinary And Partial Differential Equations Of Fractional Order
• Cauchy-type And Dirichlet-type Problems
• Laplace And Fourier And Mellin Transforms
• Mittag-Leffler Function