Geodesic
Existence and uniqueness of the solution to a class of fractional boundary value problems using topological methods
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 15 (2022) no. 5, pp. 615-622.

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This paper investigates the existence and uniqueness of solutions to boundary value problems involving the Caputo fractional derivative in Banach space by topological structures with some appropriate conditions. It is based on the application of topological methods and fixed point theorems. Moreover, some topological properties of the solutions set are considered. Finally, an example is provided to illustrate the main results.
Keywords: fractional derivatives and integrals, topological properties of mappings, fixed point theorems. 
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Taghareed A. Faree; Satish K. Panchal. Existence and uniqueness of the solution to a class of fractional boundary value problems using topological methods. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 15 (2022) no. 5, pp. 615-622. http://geodesic.mathdoc.fr/item/JSFU_2022_15_5_a7/

[1] R.P. Agarwal, M. Benchohra, S. Hamani, “A survey on existence results for boundary value problems of nonlinear fractional differential equations and inclusions”, Acta. Appl. Math., 109 (2010), 973–1033 | DOI | MR | Zbl

[2] R.P. Agarwal, Y. Zhou, Y. He, “Existence of fractional neutral functional differential equations”, Comput. Math. Appl., 59 (2010), 1095–1100 | DOI | MR | Zbl

[3] A.B. Malinowska, D.F.M. Torres, Introduction to the Fractional Calculus of Variations, World Scientific, 2012 | MR

[4] K. Balachandran, J.Y. Park, “Nonlocal Cauchy problem for abstract fractional semilinear evolution equations”, Nonlinear Analysis, 71 (2009), 4471–4475 | DOI | MR | Zbl

[5] M. Benchohra, A. Cabada, D. Seba, An Existence Result for Nonlinear Fractional Differential Equations on Banach Spaces, Hindawi Publishing Corporation, 2009 | MR

[6] M. Feckan, Topological Degree Approach to Bifurcation Problems, Topological Fixed Point Theory and its Applications, 5, 2008 | MR | Zbl

[7] J. Mawhin, Topological Degree Methods in Nonlinear Boundary Value Problems, CMBS Regional Conference Series in Mathematics, 40, Amer. Math. Soc., Providence, R.I., 1979 | DOI | MR | Zbl

[8] R.A. Khan, K. Shah, “Existence and uniqueness of solutions to fractional order multi-point boundary value problems”, Comun. Appl. Anal., 19 (2015), 515–526 | MR

[9] A.A. Kilbas, H.M. Srivastava, J.J. Trujillo, Theory and applications of fractional differential equations, North-Holland Mathematics Studies, Elsevier, Amsterdam, 2006 | MR | Zbl

[10] K.S. Miller, B. Ross, An Introduction to the Fractional Calculus and Differential Equations, John Wiley, New York, 1993 | MR | Zbl

[11] I. Podlubny, Fractional Differential Equation, Academic Press, San Diego, 1999 | MR

[12] Samina, K. Shah, R.A. Khan, “Existence of positive solutions to a coupled system with three point boundary conditions via degree theory”, Communications in Nonlinear Analysis, 3 (2017), 34–43

[13] T.A. Faree, S.K. Panchal, “Fractional Boundary Value Problems with Integral Boundary Conditions via Topological Degree Method”, Journal of Mathematical Research with Applications, 42:2 (2022), 145–152 | MR | Zbl

[14] T.A. Faree, S.K. Panchal, “Existence of solution for impulsive fractional differential equations via topological degree method”, J. Korean Soc. Ind. Appl. Math., 25:1 (2021), 16–25 | MR | Zbl

[15] T.A. Faree, S.K. Panchal, “Existence of solution to fractional hybrid differential equations using topological degree theory”, J. Math. Comput. Sci., 12 (2022), 170 | MR

[16] T.A. Faree, S.K. Panchal, “Approximative Analysis for Boundary Value Problems of Fractional Order via Topological Degree Method”, Annals of Pure and Applied Mathematics, 25:1 (2022), 7–15 | MR

[17] J. Wang, Y. Zhou, W. Wei, “Study in fractional differential equations by means of topological degree methods”, Numerical functional analysis and optimization, 33:2 (2012) | DOI | MR

[18] J. Wang, Y. Zhou, M. Medve, “Qualitative analysis for nonlinear fractional differential equations via topological degree method”, Topological methods in Nonlinear Analysis, 40:2 (2012), 245–271 | MR | Zbl

[19] S. Zhang, “Positive solutions for boundary-value problems of nonlinear fractional differential equations”, Electron. J. Differ. Equ., 36 (2006), 1–12 | DOI | MR

[20] S. Zhang, “The existence of a positive solution for a nonlinear fractional differential equation”, J. Math. Anal. Appl., 252 (2000), 804–812 | DOI | MR | Zbl

[21] Y. Zhou, Basic Theory Of Fractional Differential Equations, World Scientific, 2017 | MR | Zbl