The existence of solutions of integral boundary value problem for Hilfer fractional differential equations with \(p\)-Laplacian at resonance. (English) Zbl 07919241
Summary: By using the extension of the continuous theorem of Ge and Ren, the solvability of integral boundary value problems for Hilfer fractional differential equations with \(p\)-Laplacian is investigated. In order to get this conclusion, we construct appropriate Banach spaces and define suitable operators. At the end of the article, an example is given to illustrate our main results.
MSC:
| 34A08 | Fractional ordinary differential equations |
| 34B15 | Nonlinear boundary value problems for ordinary differential equations |
Keywords:
Hilfer fractional derivative; continuous theorem; \(p\)-Laplacian; resonance; boundary value problemReferences:
| [1] | A. Atangana, A. Akgü and K. M. Owolabi, Analysis of fractal fractional dif-ferential equations, Alexandria Engineering Journal, 2020, 59(3), 1117-1134. |
| [2] | R. P. Agarwal, M. Belmekki and M. Benchohra, Survey on semi-linear differen-tial equations and inclusions involving Riemann-Liouville fractional derivative, Adv. Differ. Equ., 2009, 1-47. · Zbl 1182.34103 |
| [3] | Y. Y. Gambo and R. Ameen, Existence and uniqueness of solutions to fractional differential equations in the frame of generalized Caputo fractional derivatives, Advances in Difference Equations, 2018, 2018(1), 134. · Zbl 1445.34013 |
| [4] | W. Ge and J. Ren, An extension of Mawhin’s continuation theorem and its application to boundary value problems with a p-Laplacian, Nonlinear Anal., 2004, 58, 477-488. · Zbl 1074.34014 |
| [5] | R. Hilfer, Applications of Fractional Calculus in Physics, World Scientific, 2000. · Zbl 0998.26002 |
| [6] | O. F. Imaga and S. A. Iyase, On a fractional-order p-Laplacian boundary value problem at resonance on the half-line with two dimensional kernel, Advances in Difference Equations, 2021, 2021(1), 1-14. · Zbl 1494.34094 |
| [7] | K. Jong, H. C. 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, Communications in Nonlinear Science and Numerical Simulation, 2019, 72, 272-281. · Zbl 1464.34020 |
| [8] | W. Jiang, J. Qiu and C. Yang, The existence of solutions for fractional differ-ential equations with p-Laplacian at resonance, An Interdisciplinary Journal of Nonlinear Science, 2017, 27(3), 032102. · Zbl 1390.34021 |
| [9] | W. Jiang, Solvability of fractional differential equations with p-Laplacian at resonance, Applied Mathematics and Computation, 2015, 260, 48-56. · Zbl 1410.34020 |
| [10] | A. A. Kilbas, H. M. Srivastava and J. J. Trujillo, Theory and applications of fractional differential equations, Elsevier, Amsterdam, 2006. · Zbl 1092.45003 |
| [11] | R. Kamocki, A new representation formula for the Hilfer fractional derivative and its application, Journal of Computational, 2016, 39-45. · Zbl 1345.26013 |
| [12] | J. Kuang, Applied Inequalities, Shandong Science and Technology Press, Jinan, 2014, 132. |
| [13] | Y. Lv, Existence of Multiple Positive Solutions for a Mixed-order Three-point Boundary Value Problem with p-Laplacian, Engineering Letters, 2020, 28(2), 428-432. |
| [14] | H. R. Marasi and H. Aydi, Existence and uniqueness results for two-term non-linear fractional differential equations via a fixed point technique, Journal of Mathematics, 2021, 2021. · Zbl 1477.34019 |
| [15] | J. Mawhin, Topological degree methods in nonlinear boundary value problems, in: NSFCBMS Regional Conference Series in Mathematics, American Mathe-matical Society, Providence, RI., 1979. · Zbl 0414.34025 |
| [16] | J. Wang and Y. Zhang, Nonlocal initial value problems for differential equations with Hilfer fractional derivative, Applied Mathematics, 2015, 266, 850-859. · Zbl 1410.34032 |
| [17] | Y. Wang and Q. Wang, Lyapunov-type inequalities for nonlinear fractional dif-ferential equation with Hilfer fractional derivative under multi-point boundary conditions, Fractional Calculus and Applied Analysis, 2018, 21(3), 833-843. · Zbl 1406.34024 |
| [18] | J. Xie and L. Duan, Existence of Solutions for Fractional Differential Equa-tions with p-Laplacian Operator and Integral Boundary Conditions, Journal of Function Spaces, 2020, 2020. · Zbl 1444.35083 |
| [19] | L. Zhang, F. Wang and Y. Ru, Existence of Nontrivial Solutions for Fractional Differential Equations with p-Laplacian, Journal of Function Spaces, 2019. · Zbl 1409.34018 |
| [20] | B. Zhou, L. Zhang, E. Addai, et al., Multiple positive solutions for nonlinear high-order RiemannšCLiouville fractional differential equations boundary value problems with p-Laplacian operator, Boundary Value Problems, 2020, 2020(1), 1-17. · Zbl 1495.34048 |
| [21] | W. Zhang, W. Liu and T. Chen, Solvability for a fractional p-Laplacian mul-tipoint boundary value problem at resonance on infinite interval, Advances in Difference Equations, 2016, 2016(1), 1-14. · Zbl 1419.34047 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
