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2022 On Nodal Properties for Some Nonlinear Conformable Fractional Differential Equations
Wei-Chuan Wang, Yan-Hsiou Cheng
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Taiwanese J. Math. Advance Publication 1-19 (2022). DOI: 10.11650/tjm/220104

Abstract

A class of conformable fractional differential equations \[ D_x^{\alpha} D_x^{\alpha} u(x) + \omega(x) f(u(x)) = 0 \quad \textrm{on $(0,1)$} \] is considered. We first give a sufficient condition for the existence of sign-changing solutions with the prescribed number of zeros to this problem. On the basis of this result, we turn to a specific case of the above problem and give a uniqueness theorem related to the function $\omega$. Essentially, the main methods using in this work are properties of conformable fractional calculus, the scaling argument and Prüfer-type substitutions.

Funding Statement

The work is partially supported by Ministry of Science and Technology, Taiwan under contract number MOST 109-2115-M-507-001 and MOST 109-2115-M-152-002.

Citation

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Wei-Chuan Wang. Yan-Hsiou Cheng. "On Nodal Properties for Some Nonlinear Conformable Fractional Differential Equations." Taiwanese J. Math. Advance Publication 1 - 19, 2022. https://doi.org/10.11650/tjm/220104

Information

Published: 2022
First available in Project Euclid: 14 February 2022

Digital Object Identifier: 10.11650/tjm/220104

Subjects:
Primary: 34A12 , 34A55 , 34B15

Keywords: conformable fractional calculus , sign-changing solution , uniqueness

Rights: Copyright © 2022 The Mathematical Society of the Republic of China

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