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Volume 4, Issue 1
Existence Results for Fractional Differential Equations with the Riesz-Caputo Derivative

Shan Wang & Zhen Wang

DOI: 10.12150/jnma.2022.114

J. Nonl. Mod. Anal., 4 (2022), pp. 114-128.

Published online: 2022-06

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

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  • Abstract

In this paper, we apply some fixed point theorems to attain the existence of solutions for fractional differential equations with the space-time Riesz-Caputo derivative. We study the boundary value problems that the nonlinearity term $f$ is relevant to fractional integral and fractional derivative. In addition, the boundary conditions involve integral. Two examples are given to show the effectiveness of theoretical results.

  • Keywords

Fractional differential equation, Riesz-Caputo derivative, Fixed point theorem.

  • AMS Subject Headings

264A33, 34B15

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JNMA-4-114, author = {Wang , Shan and Wang , Zhen}, title = {Existence Results for Fractional Differential Equations with the Riesz-Caputo Derivative}, journal = {Journal of Nonlinear Modeling and Analysis}, year = {2022}, volume = {4}, number = {1}, pages = {114--128}, abstract = {

In this paper, we apply some fixed point theorems to attain the existence of solutions for fractional differential equations with the space-time Riesz-Caputo derivative. We study the boundary value problems that the nonlinearity term $f$ is relevant to fractional integral and fractional derivative. In addition, the boundary conditions involve integral. Two examples are given to show the effectiveness of theoretical results.

}, issn = {2562-2862}, doi = {https://doi.org/10.12150/jnma.2022.114}, url = {http://global-sci.org/intro/article_detail/jnma/20697.html} }
TY - JOUR T1 - Existence Results for Fractional Differential Equations with the Riesz-Caputo Derivative AU - Wang , Shan AU - Wang , Zhen JO - Journal of Nonlinear Modeling and Analysis VL - 1 SP - 114 EP - 128 PY - 2022 DA - 2022/06 SN - 4 DO - http://doi.org/10.12150/jnma.2022.114 UR - https://global-sci.org/intro/article_detail/jnma/20697.html KW - Fractional differential equation, Riesz-Caputo derivative, Fixed point theorem. AB -

In this paper, we apply some fixed point theorems to attain the existence of solutions for fractional differential equations with the space-time Riesz-Caputo derivative. We study the boundary value problems that the nonlinearity term $f$ is relevant to fractional integral and fractional derivative. In addition, the boundary conditions involve integral. Two examples are given to show the effectiveness of theoretical results.

Shan Wang & Zhen Wang. (2022). Existence Results for Fractional Differential Equations with the Riesz-Caputo Derivative. Journal of Nonlinear Modeling and Analysis. 4 (1). 114-128. doi:10.12150/jnma.2022.114
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