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Monotone method for discrete fractional boundary value problems | ||
International Journal of Nonlinear Analysis and Applications | ||
مقاله 159، دوره 13، شماره 2، مهر 2022، صفحه 1989-1997 اصل مقاله (430.99 K) | ||
نوع مقاله: Research Paper | ||
شناسه دیجیتال (DOI): 10.22075/ijnaa.2022.19551.2086 | ||
نویسندگان | ||
Buse Eralp؛ Fatma Serap Topal* | ||
Department of Mathematics, Ege University, 35100 Bornova, Izmir, Turkey | ||
تاریخ دریافت: 23 دی 1398، تاریخ بازنگری: 03 اسفند 1400، تاریخ پذیرش: 15 خرداد 1401 | ||
چکیده | ||
In this paper, by using the Schauder fixed point theorem, we obtain the existence of positive solutions for discrete fractional boundary value problem. Also, we establish upper and lower solution for this problem. Our results extend some recent works in the literature. | ||
کلیدواژهها | ||
Positive solutions؛ Discrete fractional equations؛ Lower and upper solutions | ||
مراجع | ||
[1] I. Areeba and A. Peterson, Green’s functions and Lyapunov inequalities for Nabla Caputo boundary value problems, PhD, University of Nebraska-Lincoln, 2018. [2] T. Atanackovi´c, S. Pilipovi´c, B. Stankovi´c and D. Zorica, Fractional calculus with applications in mechanics: Vibrations and diffusion processes, Wiley, 2014. [3] F.M. Atici and P.W. Eloe, A transform method in discrete fractional calculus, Int. J. Difference Equ. 2 (2007), 165–176. [4] R. Chaudhary, V. Singh and D.N. Pandey, Controllability of multi-term time-fractional differential systems with state-dependent delay, J. Appl. Anal. 26 (2020), no. 2, 241–255. [5] X.L. Ding and Y.L. Jiang YL, Waveform relaxation methods for fractional functional differential equations, Fract. Calc. Appl. Anal. 16 (2013), no. 3, 573–594. [6] B. Eralp and F.S. Topal, Existance of Positive for Discrete Fractional Boundary Value Problems, ADSA 15 (2020), no. 2, 79–97. [7] G. Folland, Real analysis: Modern techniques and their apllications, John Wiley and Sons, Inc., New York (Second Edition), 1999. [8] S.C. Goodrich, Solutions to a discrete right-focal fractional boundary value problem, Int. J. Difference Equ. 5 (2010), no. 2, 195–216. [9] S.C. Goodrich and A. Peterson, Discrete Fractional Calculus, Springer, 2015. [10] J. Guy, On the derivative chain-rules in fractional calculus via fractional difference and their application to systems modelling, Open Phys. 11 (2016), no. 6, 617–633. [11] R.W. Ibrahim and H.A. Jalab, Existence of a class of fractional difference equations with two point boundary value problem, Adv. Differ. Equ. 2015 (2015), Article Number 269. [12] W. Lv, Existence of solutions for discrete fractional boundary value problems with a p-Laplacian operator, Adv. Differ. Equ. 2012 (2012), Article Number 163, 1–10. [13] K.S. Mille and B. Ross, An introduction to the fractional calculus and fractional differential equations, Wiley, New York, 1993. [14] J.J. Nieto and J. Pimentel, Positive solutions of a fractional thermostat model, Bound. Value Probl. 2013 (2013), Article Number 5. [15] K.S. Nisar, D. Baleanu and M.M.A. Qurashi, Fractional calculus and application of generalized Struve function, SpringerPlus 5 (2016), no. 1, 1–13. [16] K.B. Oldham and J. Spanier, The fractional calculus: Theory and applications of differentiation and integration to arbitrary order, Dover, New York, 2002. [17] K. Virginia, The special functions of fractional calculus as generalized fractional calculus operators of some basic functions, Comput. Math. Appl. 59 (2010), no. 3, 1128–1141. | ||
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