Existence results for fractional order boundary value problem with nonlocal non-separated type multi-point integral boundary conditions

Nayyar Mehmood; Niaz Ahmad

doi:10.3934/math.2020026

AIMS Mathematics, 2020, 5(1): 385-398. doi: 10.3934/math.2020026. Research article Special Issues

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Existence results for fractional order boundary value problem with nonlocal non-separated type multi-point integral boundary conditions

Nayyar Mehmood, Niaz Ahmad

Department of Mathematics and Statistics, International Islamic University, H-10, Islamabad, Pakistan

Received: , Accepted: , Published:

Special Issues: Initial and Boundary Value Problems for Differential Equations

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In this article, we discuss the existence of solutions of a fractional boundary value problem of order m ∈ (1, 2], with nonlocal non-separated type integral multipoint boundary conditions. Shaefer type and Krasnoselskii’s fixed point theorems are used to prove existence results for the given problem. To establish the uniqueness of solutions Banach contraction principle is used. The criteria for HyersUlam stability of the given boundary value problem is also discussed. Some examples are included for the illustration of our results.

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Keywords: nonlocal; non-separated; fractional BVP; existence; unique solution; Hyers-Ulam stability

Citation: Nayyar Mehmood, Niaz Ahmad. Existence results for fractional order boundary value problem with nonlocal non-separated type multi-point integral boundary conditions. AIMS Mathematics, 2020, 5(1): 385-398. doi: 10.3934/math.2020026

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