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Nyamoradi, Nemat; Ahmad, Bashir

Solvability of Hadamard fractional differential equations on a half-line with logarithmic type initial data. (English) Zbl 07924017

J. Appl. Anal. Comput. 14, No. 3, 1613-1624 (2024).
Summary: In this paper, by using the Leray-Schauder nonlinear alternative and contraction mapping principle, we study the existence and uniqueness of solutions to a new class of Hadamard fractional differential equations on a half-line supplemented with logarithmic type initial conditions.

MSC:

47H10 Fixed-point theorems
26A33 Fractional derivatives and integrals
34A08 Fractional ordinary differential equations

Keywords:

Hadamard fractional derivative; logarithmic type initial data; existence of solutions; fixed point
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References:

[1] R. P. Agarwal, M. Meehan and D. Oregan, Fixed Point Theory and Applica-tions, Cambridge University Press, Cambridge, 2001. · Zbl 0960.54027
[2] B. Ahmad, R. P. Agarwal, A. Broom and A. Alsaedi, On a coupled integro-differential system involving mixed fractional derivatives and integrals of differ-ent orders, Miskolc Math. Notes Acta Mathematica Scientia. Series B, English Edition, 2021, 41(4), 1366-1384. · Zbl 1524.45009
[3] B. Ahmad, A. Alsaedi, S. K. Ntouyas and J. Tariboon, Hadamard-Type Frac-tional Differential Equations, Inclusions and Inequalities, Springer, Cham, 2017. · Zbl 1370.34002
[4] T. S. Cerdik and F. Y. Deren, New results for higher-order Hadamard-type fractional differential equations on the half-line, Mathematical Methods in the Applied Sciences, 2021. DOI: 10.1002/mma.7926. · Zbl 1527.34022 · doi:10.1002/mma.7926
[5] A. Granas, R. B. Guenther and J. W. Lee, Some general existence principle in the Carathéodory theory of nonlinear systems, Journal de Mathématiques Pures et Appliquées, 1991, 70, 153-196. · Zbl 0687.34009
[6] J. Hadamard, Essai sur l’étude des fonctions donnees par leur developpment de Taylor, Journal de Mathématiques Pures et Appliquées, 1892, 8, 101-186. · JFM 24.0359.01
[7] A. A. Kilbas, H. M. Srivastava and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier, Amsterdam, 2006. · Zbl 1092.45003
[8] S. Liang and J. Zhang, Existence of three positive solutions of m-point bound-ary value problems for some nonlinear fractional differential equations on an infinite interval, Computers Mathematics with Applications, 2011, 61, 3343-3354. · Zbl 1235.34079
[9] S. Liang and J. Zhang, Existence of multiple positive solutions for m-point fractional boundary value problems on an infinite interval, Mathematical and Computer Modelling, 2011, 54, 1334-1346. · Zbl 1235.34023
[10] Y. Liu, Existence and uniqueness of solutions for a class of initial value problems of fractional differential systems on half lines, Bulletin des Sciences Mathématiques, 2013, 137, 1048-1071. · Zbl 1286.34012
[11] Y. Liu, B. Ahmad and R. P. Agarwal, Existence of solutions for a coupled system of nonlinear fractional differential equations with fractional boundary conditions on the half-line, Advances in Difference Equations, 2013, 46(2013), 19. · Zbl 1380.34015
[12] P. Thiramanus, S. K. Ntouyas and J. Tariboon, Positive solutions for Hadamard fractional differential equations on infinite domain, Advances in Dif-ference Equations, 2016, (2016), 118. · Zbl 1348.34025
[13] G. Wang, iteration and unbounded solutions for fractional integral boundary value problem on an infinite interval, Applied Mathematics Letters, 2015, 47, 1-7. · Zbl 1325.34015
[14] G. Wang, K. Pei, R. P. Agarwal, L. Zhang and B. Ahmad, Nonlocal Hadamard fractional boundary value problem with Hadamard integral and discrete bound-ary conditions on a half-line, Journal of Computational and Applied Mathe-matics, 2018, 343, 230-239. · Zbl 1524.34057
[15] C. Zhai and J. Ren, A coupled system of fractional differential equations on the half-line, Boundary Value Problems, 2019, 117(2019), 22. · Zbl 1513.34045
[16] L. Zhang, B. Ahmad, G. Wang and R. P. Agarwal, Nonlinear fractional integro-differential equations on unbounded domains in a Banach space, Journal of Computational and Applied Mathematics, 2013, 249, 51-56. · Zbl 1302.45019
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