Smallest eigenvalues for boundary value problems of two term fractional differential operators depending on fractional boundary conditions
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Date
2021-07-07
Authors
Eloe, Paul W.
Neugebauer, Jeffrey T.
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
Let n ≥ 2 be an integer, and let n - 1 < α ≤ n. We consider eigenvalue problems for two point n - 1, 1 boundary value problems
Dα0+ u + α(t)u + λp(t)u = 0, 0 < t < 1,
u(i)(0) = 0, i = 0, 1,..., n - 2, Dβ0+ u(1) = 0,
where 0 ≤ β ≤ n - 1 and Dα0+ and Dβ0+ denote standard Riemann-Liouville differential operators. We prove the existence of smallest positive eigenvalues and then obtain comparisons of these smallest eigenvalues as functions of both p and β.
Description
Keywords
Riemann-Liouville fractional differential equation, Boundary value problem, Principal eigenvalue, Fractional boundary conditions
Citation
Eloe, P. W., & Neugebauer, J. T. (2021). Smallest eigenvalues for boundary value problems of two term fractional differential operators depending on fractional boundary conditions. <i>Electronic Journal of Differential Equations, 2021</i>(62), pp. 1-14.
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Attribution 4.0 International