Nonlinear singular $ p $ -Laplacian boundary value problems in the frame of conformable derivative

Mokhtar Bouloudene; Manar A. Alqudah; Fahd Jarad; Yassine Adjabi; Thabet Abdeljawad

doi:10.3934/dcdss.2020442

Article Contents

2021, Volume 14, Issue 10: 3497-3528. Doi: 10.3934/dcdss.2020442

This issue Previous Article On a nonlocal problem involving the fractional

$ p(x,.) $

-Laplacian satisfying Cerami condition Next Article On the fuzzy stability results for fractional stochastic Volterra integral equation

Nonlinear singular $ p $ -Laplacian boundary value problems in the frame of conformable derivative

1.
Department of Mathematics, Faculty of Sciences University of Bougara, U.M.B.B., Algeria
2.
Dynamic of Engines and Vibroacoustic Laboratory, U.M.B.B., Algeria
3.
Department of Mathematical Sciences, Princess Nourah Bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia
4.
Department of Mathematics, Çankaya University 06790, Ankara, Turkey
5.
Department of Mathematics, Faculty of Sciences University of M'hamed Bougara, UMBB, Algeria
6.
Laboratory of Dynamical Systems, Faculty of Mathematics, U.S.T.H.B., Algeria
7.
Department of Mathematics and Physical Sciences, Prince Sultan University, P. O. Box 66833, Riyadh, 11586, KSA
8.
Department of Medical Research, China Medical University, 40402, Taichung, Taiwan
9.
Department of Computer Science and Information Engineering, Asia University, Taichung, Taiwan

^* Corresponding author: tabdeljawad@psu.edu.sa
^* Corresponding author: tabdeljawad@psu.edu.sa

Received: October 31, 2019

Revised: March 31, 2020

Early access: November 2020

Published: October 2021

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Abstract

This paper studies a class of fourth point singular boundary value problem of $ p $-Laplacian operator in the setting of a specific kind of conformable derivatives. By using the upper and lower solutions method and fixed point theorems on cones., necessary and sufficient conditions for the existence of positive solutions are obtained. In addition, we investigate the dependence of the solution on the order of the conformable differential equation and on the initial conditions.

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Mathematics Subject Classification: Primary: 26A33; Secondary: 34B16, 34B18, 47H10.

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