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Fractal Fract
Volume 8
Issue 7
10.3390/fractalfract8070377
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This is an early access version, the complete PDF, HTML, and XML versions will be available soon.
Article

Positive Solutions and Their Existence of a Nonlinear Hadamard Fractional-Order Differential Equation with a Singular Source Item Using Spectral Analysis

by
Cheng Li
1 and
Limin Guo
2,*
1
School of Automotive Engineering, Changzhou Institute of Technology, Changzhou 213032, China
2
School of Science, Changzhou Institute of Technology, Changzhou 213032, China
*
Author to whom correspondence should be addressed.
Fractal Fract. 2024, 8(7), 377; https://doi.org/10.3390/fractalfract8070377
Submission received: 27 May 2024 / Revised: 23 June 2024 / Accepted: 25 June 2024 / Published: 26 June 2024
(This article belongs to the Special Issue Numerical Solution and Applications of Fractional Differential Equations, 2nd Edition)
Versions Notes

Abstract

Based on the spectral analysis method, Gelfand’s formula, and the cones fixed point theorem, some positive solutions with their existence of a nonlinear infinite-point Hadamard fractional-order differential equation is achieved on the interval [a, b] under some conditions, and particularly the nonlinear term allows singularities for time and spatial parameters in the present study. Finally, an analysis case is carried out to reveal the principal results.
Keywords: hadamard; fractional-order differential; positive solution; infinite-point; specral analysis hadamard; fractional-order differential; positive solution; infinite-point; specral analysis

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MDPI and ACS Style

Li, C.; Guo, L. Positive Solutions and Their Existence of a Nonlinear Hadamard Fractional-Order Differential Equation with a Singular Source Item Using Spectral Analysis. Fractal Fract. 2024, 8, 377. https://doi.org/10.3390/fractalfract8070377

AMA Style

Li C, Guo L. Positive Solutions and Their Existence of a Nonlinear Hadamard Fractional-Order Differential Equation with a Singular Source Item Using Spectral Analysis. Fractal and Fractional. 2024; 8(7):377. https://doi.org/10.3390/fractalfract8070377

Chicago/Turabian Style

Li, Cheng, and Limin Guo. 2024. "Positive Solutions and Their Existence of a Nonlinear Hadamard Fractional-Order Differential Equation with a Singular Source Item Using Spectral Analysis" Fractal and Fractional 8, no. 7: 377. https://doi.org/10.3390/fractalfract8070377

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