Existence Results of Nonlinear Fractional Differential Equations with Nonlocal Conditions

Abstract

This paper explores a new class of nonlinear fractional differential equations coupled with integral terms and nonlocal boundary conditions. We consider ^cD^Φψ(ρ) = H(ρ,ψ(ρ),(ϒψ)(ρ)), ρ ∈ [0,ϖ], 1 < φ ≤ 2, subject to the following conditions ψ(h) = −ψ(ϖ), ψ'(h) = −ψ'(ϖ), 0 ≤ h < ϖ. The focus is on establishing the existence and uniqueness of solutions using a combination of fixed point theorems and the contraction principals. Our results extend some previous work and contribute to understanding fractional differential equations with complex boundary behaviors, offering new insights into their applications.