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Volume 5, Issue 4
Positive Solutions for Hilfer Fractional Differential Equation Boundary Value Problems at Resonance

Zhiyuan Liu & Shurong Sun

DOI: 10.12150/jnma.2023.695

J. Nonl. Mod. Anal., 5 (2023), pp. 695-707.

Published online: 2023-12

[An open-access article; the PDF is free to any online user.]

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  • Abstract

In this paper, we investigate the positive solutions for Hilfer fractional differential equation boundary value problems at resonance. First, we give the expression of the solution with Mittag-Leffler function. Next, we obtain the existence of the positive solutions by using fixed point index theorem. Finally, we give relevant examples to prove our main results.

  • Keywords

Fractional differential equation, resonance, Hilfer fractional derivative, positive solution, fixed point index.

  • AMS Subject Headings

34A08, 34F15, 74G10, 34B18, 37C25

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JNMA-5-695, author = {Liu , Zhiyuan and Sun , Shurong}, title = {Positive Solutions for Hilfer Fractional Differential Equation Boundary Value Problems at Resonance}, journal = {Journal of Nonlinear Modeling and Analysis}, year = {2023}, volume = {5}, number = {4}, pages = {695--707}, abstract = {

In this paper, we investigate the positive solutions for Hilfer fractional differential equation boundary value problems at resonance. First, we give the expression of the solution with Mittag-Leffler function. Next, we obtain the existence of the positive solutions by using fixed point index theorem. Finally, we give relevant examples to prove our main results.

}, issn = {2562-2862}, doi = {https://doi.org/10.12150/jnma.2023.695}, url = {http://global-sci.org/intro/article_detail/jnma/22202.html} }
TY - JOUR T1 - Positive Solutions for Hilfer Fractional Differential Equation Boundary Value Problems at Resonance AU - Liu , Zhiyuan AU - Sun , Shurong JO - Journal of Nonlinear Modeling and Analysis VL - 4 SP - 695 EP - 707 PY - 2023 DA - 2023/12 SN - 5 DO - http://doi.org/10.12150/jnma.2023.695 UR - https://global-sci.org/intro/article_detail/jnma/22202.html KW - Fractional differential equation, resonance, Hilfer fractional derivative, positive solution, fixed point index. AB -

In this paper, we investigate the positive solutions for Hilfer fractional differential equation boundary value problems at resonance. First, we give the expression of the solution with Mittag-Leffler function. Next, we obtain the existence of the positive solutions by using fixed point index theorem. Finally, we give relevant examples to prove our main results.

Zhiyuan Liu & Shurong Sun. (2023). Positive Solutions for Hilfer Fractional Differential Equation Boundary Value Problems at Resonance. Journal of Nonlinear Modeling and Analysis. 5 (4). 695-707. doi:10.12150/jnma.2023.695
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