On the Study of Ψ-Caputo Fractional Neutral Functional Differential Equation
DOI:
https://doi.org/10.18311/jims/2024/32507Keywords:
Fractional Neutral Differential Equations, Ψ−Caputo Fractional Derivative, Existence, Stability, Fixed Point Theorem.Abstract
This paper is devoted in the study of the existence, uniqueness and stabilities of solutions for Ψ-Caputo fractional neutral functional differential equation.
Downloads
Metrics
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2024 SHABNA M S MANJALINGAL HOUSE, Dr. M C RANJINI
This work is licensed under a Creative Commons Attribution 4.0 International License.
Accepted 2023-10-21
Published 2024-07-01
References
R. P. Agarwal, Yong Zhou, Yunyun He, Existence of fractional neutral functional differential equations, Computers and Mathematics with Applications, 59 (2010), 1095-1100.
Ricardo Almeida, A Caputo fractional derivative of a function with respect to another function, Commun. in Nonlinear Sci. and Num. Simulation, 44 (2017), 460-481.
Ricardo Almeida, Fractional differential equations with mixed boundary conditions, The Bulletin of the Malaysian Mathematical Society, 2 (2018)1687–1697.
Ricardo Almeida, Agnieszka B. Malinowska, M. Teresa T. Monteiro, Fractional differential equations with a Caputo derivative with respect to a Kernel function and their applications, Mathematical Methods in the Appl. Sci., WILEY, 41 (2018), 336-352.
Mehdi Dalir, Majid Bashour, Applications of Fractional Calculus, Applied Mathematical Sciences, 4 (2010), 1021-1032.
A. A. Kilbas, H. M. Srivastava and J. J. Trujillo, Theory and applications of Fractional Differential equations, North-Holland Mathematics Studies, 204, Elsevier Science B. V.,Amsterdam, 2006.
J. A. Tenreiro Machado, Manuel F. Silva, Ramiros S. Barbosa, Isabel S. Jesus, Cecilia M Reis, Maria G. Marcos and Alexandra F. Galhano, Some applications of Fractional calculus in Engineering, Mathematical Problems in Engineering, (2010) Article ID 639801.
William R. Melvin. A class of Neutral Functional Differential Equations, Journal of Differential Equations, 12 (1972), 524-534.
William R. Melvin, Some extensions of Krasnoselskii Fixed point theorem, Journal of Differential Equations, 11, (1972), 335-348.
M. S. Shabna and M. C. Ranjini, A k-dimensional systems of fractional neutral functional differential equations involving ψ− Caputo fractional derivative, Acta Universitatis Matthiae Belii series Mathematics, 28 (2020), 85–97.
M. S. Shabna and M. C. Ranjini, Fractional impulsive neutral functional differential equations involving ψ−Caputo fractional derivative. Malaya Journal of Matematik (MJM) 1 (2019), 493-499.
Vanterler da Costa Sousa J, Capelas de Oliveira E. A Gronwall inequality and the Cauchy-type problem by means of ψ-Hilfer operator, Differ. Equ. Appl. 11 (1) (2019), 87–106.
Runping Ye, Guowei Zhang. Neutral Functional Differential Equations of Second order with infinite Delays, Electronic Journal of Differential Equations, 36 (2010), 1-12.
Yong Zhang, Samantha E. Hansen, A review of applications of fractional calculus in Earth system dynamics, Chaos, Solitons and Fractals, 102 (2017), 29-46.