Positive solutions of p-Laplacian fractional differential equations with integral boundary value conditions

Abstract

In this work, we investigate the existence of solutions of p-Laplacian fractional differential equations with integral boundary value conditions. Using the five functionals fixed point theorem, the existence of multiple positive solutions is obtained for the boundary value problems. An example is also given to illustrate the effectiveness of our main result.

Analysis of p‐Laplacian Hadamard fractional boundary value problems with the derivative term involved in the nonlinear term

“…[20][21][22][23][24] Recently, there has been an increasing interest in Riemann Liouville and Caputo fractional boundary value problems involving the p-Laplacian operator, such as previous works. 8,18,19,[25][26][27][28][29] Generally, existence results of solutions are obtained for Hadamard fractional differential equations without considering the p-Laplacian operator. 9,22,[30][31][32] Furthermore, the work on existence of solutions for p-Laplacian Hadamard fractional boundary value problems whose nonlinear term 𝑓 depending on the Hadamard fractional derivative is in initial stage.…”

“…Nonlinear fractional boundary value problems including the Hadamard fractional derivative are an open research area 20–24 . Recently, there has been an increasing interest in Riemann Liouville and Caputo fractional boundary value problems involving the p‐Laplacian operator, such as previous works 8,18,19,25–29 . Generally, existence results of solutions are obtained for Hadamard fractional differential equations without considering the p‐Laplacian operator 9,22,30–32 .…”

Existence criteria of positive solutions for fractional p-Laplacian boundary value problems

“…In recent years, the subject of fractional calculus and fractional differential equations has obtained a considerable popularity and importance, mostly by virtue of their demonstrated applications in widespread fields of science and engineering. For the related applications and details about fractional calculus and fractional differential equation, see [1,2,[4][5][6][7][8][9][10][11][12][13][14][15][16] and the references therein. In [7], the authors studied the following fractional boundary value problem…”

Green's functions for boundary value problems of generalized fractional differential equations with p-Laplacian

“…Models based on generalized fractional derivatives may be more accurate than the models based on classical fractional derivatives. There exist a substantial number of papers committed to the existence of solutions for the equations with p-Laplacian operators [10,20].…”