Positive solutions of boundary value problems for p-Laplacian fractional differential equations

Abstract

This work is devoted to the existence of positive solutions for nonlinear fractional differential equations with p-Laplacian operator. By using five functionals fixed point theorem, the existence of at least three positive solutions are obtained. As an application, an example is presented to demonstrate 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 .…”

SOLVABILITY FOR A CLASS OF NONLINEAR CAPUTO-HADAMARD FRACTIONAL DIFFERENTIAL EQUATIONS WITH p-LAPLACIAN OPERATOR IN BANACH SPACES

“…Since then, fractional differential equations and the differential equation with a p-Laplacian operator are widely applied in different fields of physics and natural phenomena, for example, non-Newtonian mechanics, fluid mechanics, viscoelasticity mechanics, combustion theory, mathematical biology, the theory of partial differential equations. Hence, there have been many published papers that are devoted to the existence of solutions of boundary value problems for the p-Laplacian operator equations, see [9,22,23,34,35,41] and their references. On the other hand, it has been noticed that most of the above-mentioned work on the topic is based on Riemann-Liouville or Caputo fractional derivatives.…”