Existence, stability and global attractivity results for nonlinear Riemann-Liouville fractional differential equations
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Bapurao C. Dhage
bcdhage@gmail.com
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John R. Graef
John-Graef@utc.edu
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Shyam B. Dhage
sbdhage4791@gmail.com
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DOI:
https://doi.org/10.56754/0719-0646.2501.023Abstract
Existence, attractivity, and stability of solutions of a non-linear fractional differential equation of Riemann-Liouville type are proved using the classical Schauder fixed point theorem and a fixed point result due to Dhage. The results are illustrated with examples.
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R. Agarwal, S. Hristova and D. O’Regan, “Basic concepts of Riemann-Liouville fractional differential equations with non-instantaneous impulses”, Symmetry, vol. 11, no. 5, pp. 1–21, 2019.
J. Banas and B. C. Dhage, “Global asymptotic stability of solutions of a functional integral equations”, Nonlinear Anal., vol. 69, no. 7, pp. 1945–1952, 2008.
B. C. Dhage, “Quadratic perturbations of periodic boundary value problems of second order ordinary differential equations”, Differ. Equ. Appl., vol. 2, no. 4, pp. 465–486, 2010.
B. C. Dhage, “Some variants of two basic hybrid fixed point theorems of Krasnoselskii and Dhage with applications”, Nonlinear Stud., vol. 25, no. 3, pp. 559–573, 2018.
B. C. Dhage, “Existence and attractivity theorems for nonlinear first order hybrid differential equations with anticipation and retardation”, Jñānābha, vol. 49, no. 2, pp. 45–63, 2019.
B. C. Dhage, “Existence and attractivity theorems for nonlinear hybrid fractional differential equations with anticipation and retardation”, J. Nonlinear Funct. Anal., Article ID 47, pp. 1–18, 2020.
B. C. Dhage, “Existence and attractivity theorems for nonlinear hybrid fractional integrodifferential equations with anticipation and retardation”, Cubo, vol. 22, no. 3, pp. 325–350, 2020.
B. C. Dhage, “Global asymptotic attractivity and stability theorems for nonlinear Caputo fractional differential equations”, J. Fract. Calc. Appl., vol. 12, no. 1, pp. 223–237, 2021.
B. C. Dhage, S. B. Dhage and J. R. Graef, “Local attractivity and stability analysis of a nonlinear quadratic fractional integral equation”, Appl. Anal., vol. 95, no. 9, pp. 1989–2003, 2016.
B. C. Dhage, S. B. Dhage and S. D. Sarkate, “Attractivity and existence results for hybrid differential equations with anticipation and retardation”, J. Math. Comput. Sci., vol. 4, no. 2, pp. 206–225, 2014.
A. Granas and J. Dugundji, Fixed Point Theory, Springer Monographs in Mathematics, New York: Springer-Verlag, 2003.
A. A. Kilbas, H. M. Srivastava and J. J. Trujillo, Theory and applications of fractional differential equations, North-Holland Mathematics Studies, Amsterdam: Elsevier Science B. V., 2006.
I. Podlubny, Fractional differential equations, Mathematics in Science and Engineering 198, San Diego: Academic Press, Inc., 1999.
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