Existence Results for ψ -Caputo Fractional Differential Equations with Boundary Conditions

Authors

  • Monickpriya C
  • Swathi D

DOI:

https://doi.org/10.23755/rm.v49i0.1436

Keywords:

fractional differential equations, Cauchy problem, Volterra condition

Abstract

In this paper, we examine the existence and uniqueness of  arrangements  of a limit esteem problem for a fractional differential equation of order α ∈ (2, 3), including a general type of fractional derivative. initially, we demonstrate a comparability between the Cauchy problem and the Volterra condition. Then, at that point, two outcomes on the existence  of arrangements are demonstrated, and we end for certain illustrative models.

References

Ahmad, B., Ntouyas, S.K A new kind of nonlocal-integral fractional boundary value problems. Bull. Malays. Math. Sci. Soc. 39, 1343–1361 (2016) DOI:10.1007/s40840-015-0233-y

Almeida, R, A Caputo fractional derivative of a function with respect to another function. Commun. Nonlinear Sci. Numer. Simul. 44, 460–481 (2017). https://doi.org/10.1016/j.cnsns.2016.09.006

Almeida, R., Malinowska, A. B., Monteiro, M. T. T. Fractional differential equations with a Caputo derivative with respect to a kernel function and their applications. Math. Meth. Appl. Sci. (in press) https://doi.org/10.1002/mma.4617

Baleanu, Dumitru, Hakimeh Mohammadi, Shahram Rezapour. A fractional differential equation model for the COVID-19 transmission by using the Caputo–Fabrizio derivative. Advances in difference equations 2020.1 (2020) 1-27.

https://doi.org/10.1186/s13662-020-02762-2

Jarad F, Abdeljawad T. Generalized fractional derivatives and Laplace transform. Discrete Cont Dyn-S. DOI:10.3934/dcdss.2020039

Kilbas AA, Srivastava HM, Trujillo JJ. Theory and applications of fractional differential equations. In: North-Holland mathematics studies, vol. 204, Amsterdam: Elsevier Science B.V. 2006.

Klafter J, Lim SC, Metzler R. Fractional dynamics in physics. Singapore: World Scientific; 2011.

Lakshmikantham, V. Vatsala, A.S. Basic Theory of Fractional Differential Equations. Nonlinear Analysis, 69,(2008) 2677-2682. https://doi.org/10.1016/j.na.2007.08.042

Podlubny I. Fractional differential equations. San Diego: Academic Press; 1999.

Samko SG, Kilbas AA, Marichev OI. Fractional integrals and derivatives, theory and applications. Yverdon: Gordon and Breach; 1993.

V lakshmikantham , A S vatsala, theory of fractional differential inequalities and applications, Communications in Applied Analysis 11 (2007) 395- 402.

V. Lakshmikantham, A.S. Vatsala, General uniqueness and monotone iterative technique for fractional differential equations, Applied Mathematics Letters, Volume 21, Issue 8, 2008, 828-834, ISSN 0893-9659.

https://doi.org/10.1016/j.aml.2007.09.006

Xixi Jia, Sanyang Liu, Xiangchu Feng, Lei Zhang; A Fractional Optimal Control Network for Image Denoising; Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), 2019, pp. 6054-6063.

DOI:10.1109/CVPR.2019.00621

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Published

2023-11-19

Issue

Vol. 49 (2023): SPECIAL ISSUE: NEW DEVELOPMENTS IN MATHEMATICS AND COMPUTER SCIENCE

Section

Volume 49-2023

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