Extended existence results of solutions for FDEs of order $ 1 < \gamma\leq 2 $

Abstract

The focus of our investigation was on determining the existence of solutions for fractional differential equations (FDEs) of order $ 1 < \gamma\leq 2 $ involving the boundary conditions $ \kappa_{0}\phi(0)+\eta_{0}\phi(v) = \mu_{0} $, and $ \kappa_{1}\phi^{'}(0)+\eta_{1}\phi^{'}(v) = \mu_{1} $, for $ \kappa_i, \eta_i, \mu_i \in \mathbb{R}^{+} $. The existence results were based on the Schauder fixed point theorem and the nonlinear alternative of the Leray-Schauder type. Examples were provided to illustrate the results.

Keywords

• fractional derivatives
• differential equations
• fractional differential equations (fdes)
• existence of solutions
• fixed-point theorem