ON ITERATIVE POSITIVE SOLUTIONS FOR A CLASS OF SINGULAR INFINITE-POINT <i>P</i>-LAPLACIAN FRACTIONAL DIFFERENTIAL EQUATION WITH SINGULAR SOURCE TERMS

Limin Guo; Ying Wang; Haimei Liu; Cheng Li; Jingbo Zhao; Hualei Chu

doi:10.11948/20230008

2023 Volume 13 Issue 5

Article Contents

Article navigation > Journal of Applied Analysis & Computation > 2023 > 13(5): 2827-2842

Next Article Previous Article

Limin Guo, Ying Wang, Haimei Liu, Cheng Li, Jingbo Zhao, Hualei Chu. ON ITERATIVE POSITIVE SOLUTIONS FOR A CLASS OF SINGULAR INFINITE-POINT P-LAPLACIAN FRACTIONAL DIFFERENTIAL EQUATION WITH SINGULAR SOURCE TERMS[J]. Journal of Applied Analysis & Computation, 2023, 13(5): 2827-2842. doi: 10.11948/20230008

Citation:

Limin Guo, Ying Wang, Haimei Liu, Cheng Li, Jingbo Zhao, Hualei Chu. ON ITERATIVE POSITIVE SOLUTIONS FOR A CLASS OF SINGULAR INFINITE-POINT P-LAPLACIAN FRACTIONAL DIFFERENTIAL EQUATION WITH SINGULAR SOURCE TERMS[J]. Journal of Applied Analysis & Computation, 2023, 13(5): 2827-2842. doi: 10.11948/20230008

ON ITERATIVE POSITIVE SOLUTIONS FOR A CLASS OF SINGULAR INFINITE-POINT P-LAPLACIAN FRACTIONAL DIFFERENTIAL EQUATION WITH SINGULAR SOURCE TERMS

1.
School of science, Changzhou Institute of Technology, Liaohe, 213002 Changzhou, China
2.
School of Automotive Engineering, Changzhou Institute of Technology, Liaohe, 213002 Changzhou, China
3.
School of Mathematicacs and Statistics, Linyi University, Linyi, 276000, Shandong, China
4.
School of science, Chongqing Normal University, Chongqing, 401331, China

Author Bio: Email: guolimin811113@163.com(L. Guo); Email: liuhm@czu.cn(H. Liu); Email: zhaojb@czu.cn(J. Zhao); Email: 2745076563@qq.com(H. Chu)
Corresponding authors: Email: lywy1981@163.com(Y. Wang); Email: licheng@czu.cn(C. Li)
Fund Project: This research was supported by the National Natural Science Foundation of China (12101086, 12271232), Changzhou Science and technology planning project(CJ20220238, CE20215057, CZ20220030), Changzhou Leading Innovative Talents Cultivation Project (CQ20220092) and major project of Basic science (Natural science) research in colleges and universities of Jiangsu Province(22KJA580001)

Abstract

Abstract

Based on properties of Green's function, the existence of unique positive solution for singular infinite-point $p$-Laplacian fractional differential system is established, moreover, an iterative sequence and convergence rate are given which are important for practical application, and an example is given to demonstrate the validity of our main results.
- fractional differential /
- iterative positive solution /
- sequential techniques /
- mixed monotone operator /
- singular problem
MSC: 34B16, 34B18

FullText(HTML)

References

[1]	A. O. Akdemir, A. Karaoglan, M. A. Ragusa and E. Set, Fractional Integral Inequalities via Atangana-Baleanu Operators for Convex and Concave Functions, Journal of Function Spaces, 2021, 2021, 1055434. Google Scholar
[2]	H. M. Ahmed and M. Ragusa., Nonlocal controllability of sobolev-type conformable fractional stochastic evolution inclusions with Clarke subdifferential, Bull. of the Malaysian Mathematical Sciences Society, 2022, 45, 3239–3253. doi: 10.1007/s40840-022-01377-y CrossRef Google Scholar
[3]	D. Baleanu, S. Etemad and S. Rezapour, On a fractional hybrid integro-differential equation with mixed hybrid integral boundary value conditions by using three operators, AEJ-Alexandria Engineering Journal, 2020, 59(1). Google Scholar
[4]	B. Bi and Y. He, Monotone iterative solutions for a coupled system of $p$-Laplacian differential equations involving the Riemann-Liouville fractional derivative, Advances in Difference Equations, 2021, 2021, 103. doi: 10.1186/s13662-020-03203-w CrossRef $p$-Laplacian differential equations involving the Riemann-Liouville fractional derivative" target="_blank">Google Scholar
[5]	A. Cabada and Z. Hamdi, Nonlinear fractional differential equations with integral boundary value conditions, Appl. Math. Comput., 2014, 228(2012), 251–257. Google Scholar
[6]	D. Guo, Y. Cho and J. Zhu, Partial ordering methods in nonlinear problems, Nov a Science Publishers, New York, 2004. Google Scholar
[7]	L. Guo, L. Liu and Y. Wu, Existence of positive solutions for singular fractional differential equations with infinite-point boundary conditions, Nonlinear Anal: Model. Control., 2016, 21(5), 635–650. doi: 10.15388/NA.2016.5.5 CrossRef Google Scholar
[8]	L. Guo, L. Liu and Y. Wu, Existence of positive solutions for singular higher-order fractional differential equations with infinite-point boundary conditions, Bound. Value Probl., 2016, 2016(1), 1–22. doi: 10.1186/s13661-015-0477-3 CrossRef Google Scholar
[9]	L. Guo, L. Liu and Y. Wu, Iterative unique positive solutions for singular p-Laplacian fractional differential equation system with several parameters, Nonlinear Anal: Model. Control., 2018, 23(2), 182–203. doi: 10.15388/NA.2018.2.3 CrossRef Google Scholar
[10]	L. Guo, J. Zhao, L. Liao and L. Liu, Existence of multiple positive solutions for a class of infinite-point singular $p$-Laplacian fractional differential equation with singular source terms, Nonlinear Analysis: Modelling and Control, 2022, 27(4), 609–629. $p$-Laplacian fractional differential equation with singular source terms" target="_blank">Google Scholar
[11]	P. Hentenryck, R. Bent and E. Upfal, An introduction to the Fractional Calculus and Fractional Differential Equations, Wiley, New York, 1993. Google Scholar
[12]	M. Jleli and B. Samet, Existence of positive solutions to an arbitrary order fractional differential equation via a mixed monotone operator method, Nonlinear Anal: Model. Control., 2015, 20(3), 367–376. doi: 10.15388/NA.2015.3.4 CrossRef Google Scholar
[13]	K. Jong, H. Choi and Y. Ri, Existence of positive solutions of a class of multi-point boundary value problems for $p$-Laplacian fractional differential equations with singular source terms, Commun Nonlinear Sci Numer Simulat, 2019, 72, 272–281. doi: 10.1016/j.cnsns.2018.12.021 CrossRef $p$-Laplacian fractional differential equations with singular source terms" target="_blank">Google Scholar
[14]	A. A. Kilbas, H. M. Srivastava and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier Science BV, Amsterdam, 2006. Google Scholar
[15]	A. Lakoud and A. Ashyralyev, Existence of solutions for weighted $p(t)$-Laplacian mixed Caputo fractional differential equations at resonance, Filomat, 2022, 36, 231–241. doi: 10.2298/FIL2201231G CrossRef $p(t)$-Laplacian mixed Caputo fractional differential equations at resonance" target="_blank">Google Scholar
[16]	R. Luca, Positive solutions for a system of fractional differential equations with $p$-Laplacian operator and multi-point boundary conditions, Nonlinear Analysis: Modelling and Control, 2018, 23(5), 771–801. doi: 10.15388/NA.2018.5.8 CrossRef $p$-Laplacian operator and multi-point boundary conditions" target="_blank">Google Scholar
[17]	A. Pd, A. Sr and B. Hr, On the approximate solutions of a class of fractional order nonlinear Volterra integro-differential initial value problems and boundary value problems of first kind and their convergence analysis, Journal of Computational and Applied Mathematics, 2020. Google Scholar
[18]	N. Phuong and L. L. V. Nguyen, Inverse source problem for Sobolev equation with fractional laplacian, Journal of Function Spaces, 2022, 36, 1035118. Google Scholar
[19]	I. Podlubny, Fractional differential equations, Academic Press, New York, 1999. Google Scholar
[20]	A. Tudorache and R. Luca, On a singular Riemann-Liouville fractional boundary value problem with parameters, Nonlinear Analysis: Modelling and Control, 2021, 26(1), 151–168. doi: 10.15388/namc.2021.26.21414 CrossRef Google Scholar
[21]	H. Wang and L. Zhang, Uniqueness methods for the higher-order coupled fractional differential systems with multi-point boundary conditions, Bulletin des Sciences Mathématiques, 2021, 166, 102935. doi: 10.1016/j.bulsci.2020.102935 CrossRef Google Scholar
[22]	W. Zhang and W. Liu, Existence of solutions for fractional differential equations with infinite point boundary conditions at resonance, Bound. Value Probl., 2018, 2018(1), 36. doi: 10.1186/s13661-018-0954-6 CrossRef Google Scholar