Existence and uniqueness of linear and non-linear fractional differential equations
*Anil Kumar MenariaCorresponding authormenaria.anilkumar@gmail.comDepartment of MathematicsBhupal Nobles’ UniversityUdaipur, Rajasthan, 313002, IndiaView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 09 Jul 2024
- Published Online:
- 16 Dec 2024
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JIM-2058
- Pages:
- 1915–1921
Abstract
Keywords
Subject Classifications
References
[1] I. Podlubny, Fractional Differential Equations, Academic Press, New York, p. 261 (1999).
[2] R. Hilfer, Applications of Fraction Calculus in Physics, World Scientific Publishing Company, Singapore, New Jersey, London, and Hong Kong, p. 87 (2000).
[3] H. M. Kilbas, J. J. Srivastava, and J. J. Trujillo, Theory and Application of Fractional Differential Equations, Elsevier, Amsterdam (2006).
[4] A. A. Chikrii and I. I. Matychyn, “On an analogue of the Cauchy formula for linear systems of arbitrary fractional order,” Dopovidi Natsional’noi Akademii Nauk Ukrainy, vol. 1, pp. 50–55 (2007).
[5] A. A. Chikrii and I. I. Matichin, “Presentation of solutions of linear systems with fractional derivatives in the sense of Riemann–Liouville, Caputo, and Miller–Ross,” J. Autom. Inform. Sci., vol. 40, no. 6, pp. 1–11 (2008).
[6] C. Bai, “Impulsive periodic boundary value problems for fractional differential equations involving Riemann–Liouville sequential fractional derivative,” J. Math. Anal. Appl., vol. 384, pp. 211–231 (2011).
[7] H. Fazli, J. J. Nieto, and F. Bahrami, “On the existence and uniqueness results for nonlinear sequential fractional differential equations,” Appl. Comput. Math., vol. 17, pp. 36–47 (2018).
[8] A. Anwar, S. Muhammad, B. Z. Mian, and S. Kamal, “Existence of solution to fractional differential equations with fractional integral type boundary conditions,” Math. Methods Appl. Sci., vol. 44, pp. 1615–1627 (2020).




