Topics in Fractional Differential Equations

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


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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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.