Fractional-order boundary value problems with Katugampola fractional integral conditions Article Swipe

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Mathematics Fixed-point theorem Uniqueness Contraction principle Nonlinear system Mathematical analysis Boundary value problem Picard–Lindelöf theorem Ordinary differential equation Contraction mapping Fractional calculus Schauder fixed point theorem Partial differential equation Integral equation Differential equation Physics Quantum mechanics

Nazım I. Mahmudov , Sedef Emin ·

YOU? · · 2018 · Open Access · · DOI: https://doi.org/10.1186/s13662-018-1538-6 · OA: W2797682154

In this paper, we study existence (uniqueness) of solutions for nonlinear fractional differential equations with Katugampola fractional integral conditions. Several fixed point theorems are used for sufficient conditions of existence (uniqueness) solutions of nonlinear differential equations such as Banach’s contraction principle, the Leray–Schauder nonlinear alternative, and Krasnoselskii’s fixed point theorem. Applications of the main results are also presented.