Document Type : Research Paper

Authors

• Boddu Muralee Bala Krushna ¹
• Kapula Rajendra Prasad ²

¹ Department of Mathematics, MVGR College of Engineering, Vizianagaram, 535 005, India

² Department of Applied Mathematics, Andhra University, Visakhapatnam, 530 003, India

Abstract

In this work, we establish the existence of at least two positive solutions for a coupled system of $p$-Laplacian fractional-order boundary value problems. Establishing the existence of positive solutions to the problem is challenging for a variety of reasons, the most important of which is a lack of compatibility with the kernel. To address these issues, we have included the necessary conditions for overcoming certain methodological hurdles on the kernel as well as adapting to the problem's nature of positivity. The method is based on the AH functional fixed point theorem.

Keywords

• Fractional derivative
• boundary value problem
• $p$-Laplacian
• Integral equation
• Kernel
• positive solution