On Higher-Order Nonlinear Fractional Elastic Equations with Dependence on Lower Order Derivatives in Nonlinearity

Abstract

The paper studied high-order nonlinear fractional elastic equations that depend on low-order derivatives in nonlinearity and established the existence and uniqueness results by using the Leray–Schauder alternative theorem and Perov’s fixed point theorem on an appropriate space under mild assumptions. Examples are given to illustrate the key results.

Keywords

• Leray–Schauder alternative theorem
• Perov’s fixed point theorem
• existence and uniqueness of solutions
• Riemann–Liouville fractional derivatives