THE EXISTENCE OF SOLUTIONS OF INTEGRAL BOUNDARY VALUE PROBLEM FOR HILFER FRACTIONAL DIFFERENTIAL EQUATIONS WITH P-LAPLACIAN AT RESONANCE

Fanmeng Meng; Weihua Jiang; Yujing Liu; Chunjing Guo

doi:10.11948/20210426

2022 Volume 12 Issue 6

Article Contents

Article navigation > Journal of Applied Analysis & Computation > 2022 > 12(6): 2268-2282

Next Article Previous Article

Fanmeng Meng, Weihua Jiang, Yujing Liu, Chunjing Guo. THE EXISTENCE OF SOLUTIONS OF INTEGRAL BOUNDARY VALUE PROBLEM FOR HILFER FRACTIONAL DIFFERENTIAL EQUATIONS WITH P-LAPLACIAN AT RESONANCE[J]. Journal of Applied Analysis & Computation, 2022, 12(6): 2268-2282. doi: 10.11948/20210426

Citation:

Fanmeng Meng, Weihua Jiang, Yujing Liu, Chunjing Guo. THE EXISTENCE OF SOLUTIONS OF INTEGRAL BOUNDARY VALUE PROBLEM FOR HILFER FRACTIONAL DIFFERENTIAL EQUATIONS WITH P-LAPLACIAN AT RESONANCE[J]. Journal of Applied Analysis & Computation, 2022, 12(6): 2268-2282. doi: 10.11948/20210426

THE EXISTENCE OF SOLUTIONS OF INTEGRAL BOUNDARY VALUE PROBLEM FOR HILFER FRACTIONAL DIFFERENTIAL EQUATIONS WITH P-LAPLACIAN AT RESONANCE

1.
College of Sciences, Hebei University of Science and Technology, Shijiazhuang, Hebei, China

Corresponding author: Email address: jianghua64@163.com(W. Jiang)
Fund Project: The authors were supported by National Natural Science Foundation of China (11775169) and National Science Foundation of Hebei Province (A2018208171)

Abstract

Abstract

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.
- Hilfer fractional derivative /
- continuous theorem /
- p-Laplacian /
- resonance /
- boundary value problem
MSC: 34A08, 34B15

FullText(HTML)

References

[1]	A. Atangana, A. Akgü and K. M. Owolabi, Analysis of fractal fractional differential equations, Alexandria Engineering Journal, 2020, 59(3), 1117-1134. Google Scholar
[2]	R. P. Agarwal, M. Belmekki and M. Benchohra, Survey on semi-linear differential equations and inclusions involving Riemann-Liouville fractional derivative, Adv. Differ. Equ., 2009, 1-47. Google Scholar
[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. doi: 10.1186/s13662-018-1594-y CrossRef Google Scholar
[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. doi: 10.1016/j.na.2004.01.007 CrossRef Google Scholar
[5]	R. Hilfer, Applications of Fractional Calculus in Physics, World Scientific, 2000. Google Scholar
[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. Google Scholar
[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. Google Scholar
[8]	W. Jiang, J. Qiu and C. Yang, The existence of solutions for fractional differential equations with p-Laplacian at resonance, An Interdisciplinary Journal of Nonlinear Science, 2017, 27(3), 032102. Google Scholar
[9]	W. Jiang, Solvability of fractional differential equations with p-Laplacian at resonance, Applied Mathematics and Computation, 2015, 260, 48-56. Google Scholar
[10]	A. A. Kilbas, H. M. Srivastava and J. J. Trujillo, Theory and applications of fractional differential equations, Elsevier, Amsterdam, 2006. Google Scholar
[11]	R. Kamocki, A new representation formula for the Hilfer fractional derivative and its application, Journal of Computational, 2016, 39-45. Google Scholar
[12]	J. Kuang, Applied Inequalities, Shandong Science and Technology Press, Jinan, 2014, 132. Google Scholar
[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. Google Scholar
[14]	H. R. Marasi and H. Aydi, Existence and uniqueness results for two-term nonlinear fractional differential equations via a fixed point technique, Journal of Mathematics, 2021, 2021. Google Scholar
[15]	J. Mawhin, Topological degree methods in nonlinear boundary value problems, in: NSFCBMS Regional Conference Series in Mathematics, American Mathematical Society, Providence, RI., 1979. Google Scholar
[16]	J. Wang and Y. Zhang, Nonlocal initial value problems for differential equations with Hilfer fractional derivative, Applied Mathematics, 2015, 266, 850-859. Google Scholar
[17]	Y. Wang and Q. Wang, Lyapunov-type inequalities for nonlinear fractional differential equation with Hilfer fractional derivative under multi-point boundary conditions, Fractional Calculus and Applied Analysis, 2018, 21(3), 833-843. Google Scholar
[18]	J. Xie and L. Duan, Existence of Solutions for Fractional Differential Equations with p-Laplacian Operator and Integral Boundary Conditions, Journal of Function Spaces, 2020, 2020. Google Scholar
[19]	L. Zhang, F. Wang and Y. Ru, Existence of Nontrivial Solutions for Fractional Differential Equations with p-Laplacian, Journal of Function Spaces, 2019. Google Scholar
[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. Google Scholar
[21]	W. Zhang, W. Liu and T. Chen, Solvability for a fractional p-Laplacian multipoint boundary value problem at resonance on infinite interval, Advances in Difference Equations, 2016, 2016(1), 1-14. Google Scholar