ON A SYSTEM OF COUPLED NONLOCAL SINGULAR FRACTIONAL BOUNDARY VALUE PROBLEMS WITH <i>δ</i>-LAPLACIAN OPERATORS

Bashir Ahmad; Rodica Luca; Ahmed Alsaedi

doi:10.11948/20210247

2023 Volume 13 Issue 1

Article Contents

Article navigation > Journal of Applied Analysis & Computation > 2023 > 13(1): 57-80

Next Article Previous Article

Bashir Ahmad, Rodica Luca, Ahmed Alsaedi. ON A SYSTEM OF COUPLED NONLOCAL SINGULAR FRACTIONAL BOUNDARY VALUE PROBLEMS WITH δ-LAPLACIAN OPERATORS[J]. Journal of Applied Analysis & Computation, 2023, 13(1): 57-80. doi: 10.11948/20210247

Citation:

Bashir Ahmad, Rodica Luca, Ahmed Alsaedi. ON A SYSTEM OF COUPLED NONLOCAL SINGULAR FRACTIONAL BOUNDARY VALUE PROBLEMS WITH δ-LAPLACIAN OPERATORS[J]. Journal of Applied Analysis & Computation, 2023, 13(1): 57-80. doi: 10.11948/20210247

ON A SYSTEM OF COUPLED NONLOCAL SINGULAR FRACTIONAL BOUNDARY VALUE PROBLEMS WITH δ-LAPLACIAN OPERATORS

1.
Nonlinear Analysis and Applied Mathematics Research Group (NAAM), Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
2.
Department of Mathematics, Gh. Asachi Technical University, 11 Blvd. Carol I, Iasi 700506, Romania

Corresponding author: Email: bashirahmad_qau@yahoo.com (B. Ahmad)

Abstract

Abstract

We investigate the existence of at least one or two positive solutions of a system of two Riemann-Liouville fractional differential equations with $ \delta $-Laplacian operators and singular nonlinearities, supplemented with coupled nonlocal boundary conditions which contain Riemann-Stieltjes integrals and several fractional derivatives of different orders. We apply the Guo-Krasnosel'skii fixed point theorem in the proof of our main existence results.
- Riemann-Liouville fractional differential equations /
- singular nonlinearities /
- nonlocal boundary conditions /
- existence /
- multiplicity
MSC: 34A08, 34B10, 34B16, 34B18, 45G15

FullText(HTML)

References

[1]	R. P. Agarwal and R. Luca, Positive solutions for a semipositone singular Riemann-Liouville fractional differential problem, Intern. J. Nonlinear Sc. Numer. Simul., 2019, 20(7-8), 823-832. doi: 10.1515/ijnsns-2018-0376 CrossRef Google Scholar
[2]	B. Ahmad, A. Alsaedi, S. K. Ntouyas and J. Tariboon, Hadamard-Type Fractional Differential Equations, Inclusions and Inequalities, Springer, Cham., 2017. Google Scholar
[3]	B. Ahmad, J. Henderson and R. Luca, Boundary Value Problems for Fractional Differential Equations and Systems, Trends in Abstract and Applied Analysis 9, World Scientific, Hackensack, New Jersey, 2021. Google Scholar
[4]	B. Ahmad and R. Luca, Existence of solutions for a sequential fractional integro-differential system with coupled integral boundary conditions, Chaos Solitons Fractals, 2017, 104, 378-388. doi: 10.1016/j.chaos.2017.08.035 CrossRef Google Scholar
[5]	B. Ahmad and R. Luca, Existence of solutions for sequential fractional integro-differential equations and inclusions with nonlocal boundary conditions, Appl. Math. Comput., 2018, 339, 516-534. Google Scholar
[6]	B. Ahmad, S. K. Ntouyas and A. Alsaedi, Sequential fractional differential equations and inclusions with semi-periodic and nonlocal integro-multipoint boundary conditions, J. King Saud Univ. Sc., 2019, 31(2), 184-193. doi: 10.1016/j.jksus.2017.09.020 CrossRef Google Scholar
[7]	A. Alsaedi, B. Ahmad, S. Aljoudi and S. K. Ntouyas, A study of a fully coupled two-parameter system of sequential fractional integro-differential equations with nonlocal integro-multipoint boundary conditions, Acta Math. Sci. Ser. B (Engl. Ed. ), 2019, 39, 927-944. Google Scholar
[8]	A. Alsaedi, R. Luca and B. Ahmad, Existence of positive solutions for a system of singular fractional boundary value problems with p-Laplacian operators, Mathematics, 2020, 8(1890), 1-18. Google Scholar
[9]	D. Baleanu, K. Diethelm, E. Scalas and J. J. Trujillo, Fractional Calculus Models and Numerical Methods, Series on Complexity, Nonlinearity and Chaos, World Scientific, Boston, 2012. Google Scholar
[10]	S. Das, Functional Fractional Calculus for System Identification and Controls, Springer, New York, 2008. Google Scholar
[11]	D. Guo and V. Lakshmikantham, Nonlinear Problems in Abstract Cones, Academic Press, New York, 1988. Google Scholar
[12]	J. Henderson and R. Luca, Boundary Value Problems for Systems of Differential, Difference and Fractional Equations, Positive Solutions, Elsevier, Amsterdam, 2016. Google Scholar
[13]	J. Henderson and R. Luca, Existence of positive solutions for a singular fractional boundary value problem, Nonlinear Anal. Model. Control, 2017, 22(1), 99-114. Google Scholar
[14]	J. Henderson, R. Luca and A. Tudorache, On a system of fractional differential equations with coupled integral boundary conditions, Fract. Calc. Appl. Anal., 2015, 18(2), 361-386. doi: 10.1515/fca-2015-0024 CrossRef Google Scholar
[15]	J. Henderson, R. Luca and A. Tudorache, Existence and nonexistence of positive solutions for coupled Riemann-Liouville fractional boundary value problems, Discrete Dyn. Nature Soc., 2016, Art. ID 2823971, 1-12. Google Scholar
[16]	J. Henderson, R. Luca and A. Tudorache, Existence of positive solutions for a system of fractional boundary value problems, in "Differential and Difference Equations with Applications", ICDDEA, Amadora, Portugal, May 2015, Selected Contributions, Editors: Sandra Pinelas, Zuzana Dosla, Ondrej Dosly, Peter E. Kloeden, Springer, 2016, 349-357. Google Scholar
[17]	J. Jiang, L. Liu and Y. Wu, Positive solutions to singular fractional differential system with coupled boundary conditions, Comm. Nonlinear Sc. Num. Sim., 2013, 18(11), 3061-3074. doi: 10.1016/j.cnsns.2013.04.009 CrossRef Google Scholar
[18]	K. S. Jong, H. C. Choi and Y. H. 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 Google Scholar
[19]	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
[20]	J. Klafter, S. C. Lim and R. Metzler, Fractional Dynamics in Physics, World Scientific, Singapore, 2011. Google Scholar
[21]	R. Luca, Positive solutions for a system of fractional differential equations with p-Laplacian operator and multi-point boundary conditions, Nonlinear Anal. Model. Control, 2018, 23(5), 771-801. doi: 10.15388/NA.2018.5.8 CrossRef Google Scholar
[22]	I. Podlubny, Fractional Differential Equations, Academic Press, San Diego, 1999. Google Scholar
[23]	J. Sabatier, O. P. Agrawal and J. A. T. Machado, Advances in Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering, Springer, Dordrecht, 2007. Google Scholar
[24]	S. G. Samko, A. A. Kilbas and O. I. Marichev, Fractional Integrals and Derivatives. Theory and Applications, Gordon and Breach, Yverdon, 1993. Google Scholar
[25]	C. Shen, H. Zhou and L. Yang, Positive solution of a system of integral equations with applications to boundary value problems of differential equations, Adv. Difference Equ., 2016, 260, 1-26. Google Scholar
[26]	A. Tudorache and R. Luca, Positive solutions for a system of Riemann-Liouville fractional boundary value problems with p-Laplacian operators, Adv. Difference Equ., 2020, 292, 1-30. Google Scholar
[27]	A. Tudorache and R. Luca, Positive solutions for a singular fractional boundary value problem, Math. Meth. Appl. Sci., 2020, 43(17), 10190-10203. doi: 10.1002/mma.6686 CrossRef Google Scholar
[28]	F. Wang, L. Liu and Y. Wu, A numerical algorithm for a class of fractional BVPs with p-Laplacian operator and singularity-the convergence and dependence analysis, Appl. Math. Comput., 2020, 382, 1-13. Google Scholar
[29]	G. Wang, X. Ren, L. Zhang and B. Ahmad, Explicit iteration and unique positive solution for a Caputo-Hadamard fractional turbulent flow model, IEEE Access, 2019, 7, 109833-109839. Google Scholar
[30]	Y. Wang, L. Liu and Y. Wu, Positive solutions for a class of higher-order singular semipositone fractional differential systems with coupled integral boundary conditions and parameters, Adv. Differ. Equ., 2014, 268, 1-24. Google Scholar
[31]	C. Yuan, D. Jiang, D. O'Regan and R. P. Agarwal, Multiple positive solutions to systems of nonlinear semipositone fractional differential equations with coupled boundary conditions, Electron. J. Qual. Theory Differ. Equ., 2012, 13, 1-17. Google Scholar