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Open AccessArticle

Existence and Stability Results for a Fractional Order Differential Equation with Non-Conjugate Riemann-Stieltjes Integro-Multipoint Boundary Conditions

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Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
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Department of Mathematics, University of Ioannina, Ioannina 45110, Greece
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Author to whom correspondence should be addressed.
Mathematics 2019, 7(3), 249; https://doi.org/10.3390/math7030249
Received: 20 February 2019 / Revised: 5 March 2019 / Accepted: 5 March 2019 / Published: 11 March 2019
We discuss the existence and uniqueness of solutions for a Caputo-type fractional order boundary value problem equipped with non-conjugate Riemann-Stieltjes integro-multipoint boundary conditions on an arbitrary domain. Modern tools of functional analysis are applied to obtain the main results. Examples are constructed for the illustration of the derived results. We also investigate different kinds of Ulam stability, such as Ulam-Hyers stability, generalized Ulam-Hyers stability, and Ulam-Hyers-Rassias stability for the problem at hand. View Full-Text
Keywords: Caputo fractional derivative; nonlocal; integro-multipoint boundary conditions; existence; uniqueness; Ulam-Hyers stability Caputo fractional derivative; nonlocal; integro-multipoint boundary conditions; existence; uniqueness; Ulam-Hyers stability
MDPI and ACS Style

Ahmad, B.; Alruwaily, Y.; Alsaedi, A.; K. Ntouyas, S. Existence and Stability Results for a Fractional Order Differential Equation with Non-Conjugate Riemann-Stieltjes Integro-Multipoint Boundary Conditions. Mathematics 2019, 7, 249.

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