A fractional q-difference equation eigenvalue problem with p(t)-Laplacian operator
Articles
Chengbo Zhai
Shanxi University
https://orcid.org/0000-0002-3619-5722
Jing Ren
Shanxi University
Published 2021-05-01
https://doi.org/10.15388/namc.2021.26.23055
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Keywords

unique solution
fractional q-difference equation
p(t)-Laplacian operator
φ – (h, e)-concave operators

How to Cite

Zhai C. and Ren J. (2021) “A fractional q-difference equation eigenvalue problem with p(t)-Laplacian operator”, Nonlinear Analysis: Modelling and Control, 26(3), pp. 482-501. doi: 10.15388/namc.2021.26.23055.

Abstract

This article is devoted to studying a nonhomogeneous boundary value problem involving Stieltjes integral for a more general form of the fractional q-difference equation with p(t)-Laplacian operator. Here p(t)-Laplacian operator is nonstandard growth, which has been used more widely than the constant growth operator. By using fixed point theorems of  φ – (h, e)-concave operators some conditions, which guarantee the existence of a unique positive solution, are derived. Moreover, we can construct an iterative scheme to approximate the unique solution. At last, two examples are given to illustrate the validity of our theoretical results.

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