Function (biology)

Fixed point

Fixed-point theorem

Ecology

Biology

Boundary value problem

Differential equation

Applied mathematics

Banach fixed-point theorem

Schauder fixed point theorem

Stability (learning theory)

Economics

Computer science

Evolutionary biology

Type (biology)

Contraction mapping

Mathematics

Mathematical analysis

Ordinary differential equation

Uniqueness

Picard–Lindelöf theorem

Finance

Fractional calculus

Order (exchange)

Contraction principle

Machine learning

Boundary Value Problems

In this paper, we prove the existence and uniqueness of solutions for the nonlocal boundary value problem (BVP) using Caputo fractional derivative (CFD). We derive Green’s function and give some estimation for it to derive our main results. The main principles applied to investigate our results are based on the Banach contraction fixed point theorem and Schauder fixed point approach. We dwell in detail on some results concerning the Hyers-Ulam (H-U) type and generalized H-U (g-H-U) type stability also for problem we are considering. We justify our results with an illustrative example.

Existence and stability results for nonlocal boundary value problems of fractional order