Chapter

Topics in Fractional Differential Equations

Volume 27 of the series Developments in Mathematics pp 115-169

Date:

Partial Hyperbolic Functional Differential Inclusions

  • Saïd AbbasAffiliated withLaboratoire de Mathématiques, Université de Saïda
  • , Mouffak BenchohraAffiliated withLaboratoire de Mathématiques, Université de Sidi Bel-Abbès
  • , Gaston M. N’GuérékataAffiliated withDepartment of Mathematics, Morgan State University

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Abstract

In this chapter, we shall present existence results for some classes of initial value problems for partial hyperbolic differential inclusions with fractional order involving the Caputo fractional derivative, when the right-hand side is convex as well as nonconvex valued. Some results rely on the nonlinear alternative of Leray–Schauder type. In other results, we shall use the fixed-point theorem for contraction multivalued maps due to Covitz and Nadler.