POSITIVE SOLUTIONS IN THE SPACE OF LIPSCHITZ FUNCTIONS TO A CLASS OF FRACTIONAL DIFFERENTIAL EQUATIONS WITH INFINITE-POINT BOUNDARY VALUE CONDITIONS

Josefa Caballero; Belén López; Kishin Sadarangani

doi:10.11948/20200240

2021 Volume 11 Issue 2

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Josefa Caballero, Belén López, Kishin Sadarangani. POSITIVE SOLUTIONS IN THE SPACE OF LIPSCHITZ FUNCTIONS TO A CLASS OF FRACTIONAL DIFFERENTIAL EQUATIONS WITH INFINITE-POINT BOUNDARY VALUE CONDITIONS[J]. Journal of Applied Analysis & Computation, 2021, 11(2): 1039-1050. doi: 10.11948/20200240

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Josefa Caballero, Belén López, Kishin Sadarangani. POSITIVE SOLUTIONS IN THE SPACE OF LIPSCHITZ FUNCTIONS TO A CLASS OF FRACTIONAL DIFFERENTIAL EQUATIONS WITH INFINITE-POINT BOUNDARY VALUE CONDITIONS[J]. Journal of Applied Analysis & Computation, 2021, 11(2): 1039-1050. doi: 10.11948/20200240

POSITIVE SOLUTIONS IN THE SPACE OF LIPSCHITZ FUNCTIONS TO A CLASS OF FRACTIONAL DIFFERENTIAL EQUATIONS WITH INFINITE-POINT BOUNDARY VALUE CONDITIONS

1.
Departamento de MatemȢticas, Universidad de Las Palmas de Gran Canaria, Campus de Tafira Baja, 35017 Las Palmas de Gran Canaria, Spain

Author Bio: Email: josefa.caballero@ulpgc.es(J. Caballero); Email: ksadaran@dma.ulpgc.es(K. Sadarangani)
Corresponding author: Email: belen.lopez@ulpgc.es(B. López)

Abstract

Abstract

The purpose of this paper is to study the existence of positive solutions to a class of fractional differential equations with infinite-point boundary value conditions. Our solutions are placed in the space of Lipschitz functions and the main tools used in the proof of the results are a sufficient condition about the relative compactness in Holder spaces and the classical Schauder fixed point theorem.
- Fractional differential equation /
- Holder spaces /
- Schauder fixed point theorem /
- positive solution
MSC: 47H10, 49L20

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References

[1]	J. Banas and R. Nalepa, On the space of functions with growths tempered by a modulus of continuity and its applications, J. Funct. Space Appl., 2013, Article ID 820437. Google Scholar
[2]	J. Caballero, M. A. Darwish and K. Sadarangani, Solvability of a quadratic integral equation of Fredholm type in Holder spaces, Elect. J. Diff. Eq., 2014, 31, 1-10. Google Scholar
[3]	I. Cabrera, J. Harjani and K. Sadarangani, Existence and uniqueness of solutions for a boundary value problem of fractional type with nonlocal integral boundary conditions in Holder spaces, Mediterr. J. Math., 2018, 15, 98. doi: 10.1007/s00009-018-1142-8 CrossRef Google Scholar
[4]	M. T. Ersoy, H. Furkan and B. Saricicek, On the solutions of some nonlinear fredholm integral equations in topological Holder spaces, Turkish World Mathematical Soc. J. Appl. Engin. Math., 2020, 10, 657-668. Google Scholar
[5]	M. T. Ersoy and H. Furkan, On the existence of the solutions of a Fredholm integral equation with a modified argument in Holder spaces, Symmetry, 10, 2018, 522, doi: 10.3390/sym10100522. Google Scholar
[6]	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. Google Scholar
[7]	V. Lakshmikantham, S. Leela and J. Vasundhara Devi, Theory of Fractional Dynamic Systems, Cambridge Academic Publishers, Cambridge, 2009. Google Scholar
[8]	H. Okrasinski-Plociniczak, L. Plociniczak, J. Rocha and K. Sadarangani, Solvability in Holder spaces of an integral equation which models dynamics of the capillary rise, J. Math. Anal. Appl., 2020, 490, Article 124237. Google Scholar
[9]	I. Podlubny, Fractional Differential Equations, Academic Press, San Diego, 1999. Google Scholar
[10]	X. Zhang, Positive solutions for a class of singular fractional differential equation with infinite-point boundary value conditions, Appl. Math., 2015, 39, 22-27. Google Scholar