EXISTENCE OF SOLUTIONS TO BOUNDARY VALUE PROBLEM FOR NONLINEAR TEMPERED FRACTIONAL DIFFERENTIAL EQUATION WITH DELAY AND P-LAPLACIAN OPERATOR

Jieqiong Wu; Hongyu Li; Yujun Cui

doi:10.11948/0385

2026 Volume 16 Issue 5

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Jieqiong Wu, Hongyu Li, Yujun Cui. EXISTENCE OF SOLUTIONS TO BOUNDARY VALUE PROBLEM FOR NONLINEAR TEMPERED FRACTIONAL DIFFERENTIAL EQUATION WITH DELAY AND P-LAPLACIAN OPERATOR[J]. Journal of Applied Analysis & Computation, 2026, 16(5): 2606-2622. doi: 10.11948/0385

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Jieqiong Wu, Hongyu Li, Yujun Cui. EXISTENCE OF SOLUTIONS TO BOUNDARY VALUE PROBLEM FOR NONLINEAR TEMPERED FRACTIONAL DIFFERENTIAL EQUATION WITH DELAY AND P-LAPLACIAN OPERATOR[J]. Journal of Applied Analysis & Computation, 2026, 16(5): 2606-2622. doi: 10.11948/0385

EXISTENCE OF SOLUTIONS TO BOUNDARY VALUE PROBLEM FOR NONLINEAR TEMPERED FRACTIONAL DIFFERENTIAL EQUATION WITH DELAY AND P-LAPLACIAN OPERATOR

1.
College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China

Author Bio: Email: 202482150039@sdust.edu.cn(J. Wu); Email: cyj720201@sdust.edu.cn(J. Cui)
Corresponding author: Email: skd992179@sdust.edu.cn(H. Li)

Abstract

Abstract

In this article, we study the existence of solutions to boundary value problem for nonlinear tempered fractional differential equation with p-Laplacian operator and delay. By introducing an appropriate operator, we establish uniqueness of the solution for this problem via the Banach contraction mapping principle and obtain several existence results by employing the Schaefer's fixed-point theorem, the Leray–Schauder principle, and the Leray–Schauder nonlinear alternative theorem. Finally, a concrete problem is provided to demonstrate the applicability of the obtained theoretical results.
- Tempered fractional derivative /
- delay /
- p-Laplacian operator /
- fixed point theorem /
- existence of solutions
MSC: 34B15, 47H11

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References

[1]	H. Ahmad, F. U. Din and M. Younis, A fixed point analysis of fractional dynamics of heat transfer in chaotic fluid layers, Journal of Computational and Applied Mathematics, 2025, 453, 116144. doi: 10.1016/j.cam.2024.116144 CrossRef Google Scholar
[2]	H. Ahmad, F. U. Din and M. Younis, Fractional order lorenz dynamics: Investigating existence and uniqueness via basic contraction, Journal of Applied Mathematics and Computing, 2025, 71(5), 6827–6858. doi: 10.1007/s12190-025-02550-9 CrossRef Google Scholar
[3]	H. Ahmad, F. U. Din and M. Younis, A novel ćirić–reich–rus fixed point approach for the existence and uniqueness criterion of a fractional-order aizawa chaotic system, Chaos, Solitons & Fractals, 2025, 200, 116932. Google Scholar
[4]	H. Ahmad, F. U. Din, M. Younis and L. Chen, A simple interpolative contraction approach for analyzing existence and uniqueness of solutions in the fractional-order king cobra model, Chaos, Solitons & Fractals, 2025, 199, 116578. Google Scholar
[5]	S. Ahmed, A. T. Azar, M. Abdel-Aty, et al., A nonlinear system of hybrid fractional differential equations with application to fixed time sliding mode control for leukemia therapy, Ain Shams Engineering Journal, 2024, 15(4), 102566. doi: 10.1016/j.asej.2023.102566 CrossRef Google Scholar
[6]	R. Almeida, N. Martins and J. Sousa, Fractional tempered differential equations depending on arbitrary kernels, AIMS Mathematics, 2024, 9(4), 9107–9127. doi: 10.3934/math.2024443 CrossRef Google Scholar
[7]	N. Anwar, I. Ahmad, A. K. Kiani, et al., Novel neuro-stochastic adaptive supervised learning for numerical treatment of nonlinear epidemic delay differential system with impact of double diseases, International Journal of Modelling and Simulation, 2025, 45(5), 1852–1874. doi: 10.1080/02286203.2024.2303577 CrossRef Google Scholar
[8]	R. Bai, K. Zhang and X. -J. Xie, Existence and multiplicity of solutions for boundary value problem of singular two-term fractional differential equation with delay and sign-changing nonlinearity, Boundary Value Problems, 2023, 2023(1), 114–135. doi: 10.1186/s13661-023-01803-5 CrossRef Google Scholar
[9]	T. Burton and C. Kirk, A fixed point theorem of Krasnoselskii-Schaefer type, Mathematische Nachrichten, 1998, 189(1), 23–31. doi: 10.1002/mana.19981890103 CrossRef Google Scholar
[10]	L. Cao, Y. Pan, H. Liang and T. Huang, Observer-based dynamic event-triggered control for multiagent systems with time-varying delay, IEEE Transactions on Cybernetics, 2022, 53(5), 3376–3387. Google Scholar
[11]	W. Chen, H. Sun, X. Li, et al., Fractional Derivative Modeling in Mechanics and Engineering, Springer, Berlin/Heidelberg, 2022. Google Scholar
[12]	C. Erbil and T. F. Serap, Existence of solutions for a delay singular high order fractional boundary value problem with sign-changing nonlinearity, Filomat, 2023, 37(21), 7275–7286. doi: 10.2298/FIL2321275C CrossRef Google Scholar
[13]	C. T. Gallan and T. F. Serap, Positive solutions for integral boundary value problems of nonlinear fractional differential equations with delay, Filomat, 2023, 37(2), 567–583. doi: 10.2298/FIL2302567C CrossRef Google Scholar
[14]	A. Granas, J. Dugundji, et al., Fixed Point Theory, Springer, New York, 2003. Google Scholar
[15]	J. He, X. Zhang, L. Liu, et al., A singular fractional kelvin–voigt model involving a nonlinear operator and their convergence properties, Boundary Value Problems, 2019, 2019(1), 1–19. doi: 10.1186/s13661-018-1115-7 CrossRef Google Scholar
[16]	A. A. Keller, Contribution of the delay differential equations to the complex economic macrodynamics, WSEAS Transactions on Systems, 2010, 9(4), 358–371. Google Scholar
[17]	H. Khan, J. Alzabut, D. Baleanu, et al., Existence of solutions and a numerical scheme for a generalized hybrid class of n-coupled modified abc-fractional differential equations with an application, AIMS Mathematics, 2023, 8(3), 6609–6625. doi: 10.3934/math.2023334 CrossRef Google Scholar
[18]	Y. Li, S. Sun, D. Yang and Z. Han, Three-point boundary value problems of fractional functional differential equations with delay, Boundary Value Problems, 2013, 2013(1), 1–15. doi: 10.1186/1687-2770-2013-1 CrossRef Google Scholar
[19]	W. Liu, L. Liu and Y. Wu, Existence of solutions for integral boundary value problems of singular hadamard-type fractional differential equations on infinite interval, Advances in Difference Equations, 2020, 2020(1), 274–296. doi: 10.1186/s13662-020-02726-6 CrossRef Google Scholar
[20]	A. D. Mali, K. D. Kucche, A. Fernandez and H. M. Fahad, On tempered fractional calculus with respect to functions and the associated fractional differential equations, Mathematical Methods in the Applied Sciences, 2022, 45(17), 11134–11157. doi: 10.1002/mma.8441 CrossRef Google Scholar
[21]	Y. Mu, L. Sun and Z. Han, Singular boundary value problems of fractional differential equations with changing sign nonlinearity and parameter, Boundary Value Problems, 2016, 2016(1), 1–18. doi: 10.1186/s13661-015-0477-3 CrossRef Google Scholar
[22]	D. Patel, M. Younis and O. P. Chauhan, New results on interpolative metric spaces and applications, FILOMAT, 2025, 39(28), 10115–10128. Google Scholar
[23]	I. Podlubny, An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications, Math. Sci. Eng., 1999, 198(340), 0924–34008. Google Scholar
[24]	M. Prokhorov and V. Ponomarenko, Encryption and decryption of information in chaotic communication systems governed by delay-differential equations, Chaos, Solitons & Fractals, 2008, 35(5), 871–877. Google Scholar
[25]	W. Qiu, O. Nikan and Z. Avazzadeh, Numerical investigation of generalized tempered-type integrodifferential equations with respect to another function, Fractional Calculus and Applied Analysis, 2023, 26(6), 2580–2601. doi: 10.1007/s13540-023-00198-5 CrossRef Google Scholar
[26]	G. U. Rahman, D. Ahmad, J. F. Gómez-Aguilar, et al., Study of caputo fractional derivative and riemann–liouville integral with different orders and its application in multi-term differential equations, Mathematical Methods in the Applied Sciences, 2025, 48(2), 1464–1502. doi: 10.1002/mma.10392 CrossRef Google Scholar
[27]	F. Sabzikar, M. M. Meerschaert and J. Chen, Tempered fractional calculus, Journal of Computational Physics, 2015, 293, 14–28. doi: 10.1016/j.jcp.2014.04.024 CrossRef Google Scholar
[28]	A. Salim, J. E. Lazreg and M. Benchohra, On tempered $(\kappa, \psi)$-Hilfer fractional boundary value problems, Pan-American Journal of Mathematics, 2024, 3, 1–20. doi: 10.28919/cpr-pajm/3-1 CrossRef $(\kappa, \psi)$-Hilfer fractional boundary value problems" target="_blank">Google Scholar
[29]	S. Shi, L. Zhang and G. Wang, Fractional non-linear regularity, potential and balayage, The Journal of Geometric Analysis, 2022, 32(8), 221–250. doi: 10.1007/s12220-022-00956-6 CrossRef Google Scholar
[30]	L. Shuai, Z. Zhixin and J. Wei, Multiple positive solutions for four-point boundary value problem of fractional delay differential equations with p-Laplacian operator, Applied Numerical Mathematics, 2021, 165, 348–356. doi: 10.1016/j.apnum.2021.03.001 CrossRef Google Scholar
[31]	S. Sivalingam and V. Govindaraj, A novel numerical approach for time-varying impulsive fractional differential equations using theory of functional connections and neural network, Expert Systems with Applications, 2024, 238, 121750. doi: 10.1016/j.eswa.2023.121750 CrossRef Google Scholar
[32]	S. SM, P. Kumar and V. Govindaraj, A novel optimization-based physics-informed neural network scheme for solving fractional differential equations, Engineering with Computers, 2024, 40(2), 855–865. doi: 10.1007/s00366-023-01830-x CrossRef Google Scholar
[33]	X. Su, Positive solutions to singular boundary value problems for fractional functional differential equations with changing sign nonlinearity, Computers and Mathematics with Applications, 2012, 64(10), 3425–3435. doi: 10.1016/j.camwa.2012.02.043 CrossRef Google Scholar
[34]	J. Wang, A. Ibrahim and D. O'Regan, Finite approximate controllability of hilfer fractional semilinear differential equations, Miskolc Mathematical Notes, 2020, 21(1), 489–507. doi: 10.18514/MMN.2020.2921 CrossRef Google Scholar
[35]	H. Xu, L. Zhang and G. Wang, Some new inequalities and extremal solutions of a Caputo–Fabrizio fractional Bagley–Torvik differential equation, Fractal and Fractional, 2022, 6(9), 488–496. doi: 10.3390/fractalfract6090488 CrossRef Google Scholar
[36]	Z. You, M. Fečkan and J. Wang, Relative controllability of fractional delay differential equations via delayed perturbation of Mittag-Leffler functions, Journal of Computational and Applied Mathematics, 2020, 378, 112939. doi: 10.1016/j.cam.2020.112939 CrossRef Google Scholar
[37]	M. Younis, H. Ahmad, M. Ozturk, et al., Unveiling fractional-order dynamics: A New method for analyzing Rössler chaos, Journal of Computational and Applied Mathematics, 2025, 468, 116639. doi: 10.1016/j.cam.2025.116639 CrossRef Google Scholar
[38]	M. Younis, A. H. Dar and N. Hussain, Revised algorithm for finding a common solution of variational inclusion and fixed point problems, FILOMAT, 2023, 37, 6949–6960. doi: 10.2298/FIL2320949Y CrossRef Google Scholar
[39]	J. Zhang, J. Wang and Y. Zhou, Numerical analysis for Klein-Gordon equation with time-space fractional derivatives, Mathematical Methods in the Applied Sciences, 2020, 43(6), 3689–3700. doi: 10.1002/mma.6147 CrossRef Google Scholar
[40]	X. Zhang, P. Chen, H. Tian and Y. Wu, Upper and lower solution method for a singular tempered fractional equation with ap-Laplacian operator, Fractal and Fractional, 2023, 7(7), 522–540. doi: 10.3390/fractalfract7070522 CrossRef Google Scholar
[41]	B. Zhou, L. Zhang, E. Addai and N. Zhang, Multiple positive solutions for nonlinear high-order Riemann–Liouville fractional differential equations boundary value problems with p-Laplacian operator, Boundary Value Problems, 2020, 2020(1), 26–43. doi: 10.1186/s13661-020-01336-1 CrossRef Google Scholar
[42]	B. Zhou, L. Zhang, G. Xing and N. Zhang, Existence–uniqueness and monotone iteration of positive solutions to nonlinear tempered fractional differential equation with p-Laplacian operator, Boundary Value Problems, 2020, 2020(1), 117–134. doi: 10.1186/s13661-020-01414-4 CrossRef Google Scholar