Existence of solutions by fixed point theorem of general delay fractional differential equation with $ p $-Laplacian operator

• Published in: AIMS mathematics Vol. 8; no. 5; pp. 10160 - 10176
• Main Authors: Kaushik, Kirti, Kumar, Anoop, Khan, Aziz, Abdeljawad, Thabet
• Format: Journal Article
• Language: English
• Published: AIMS Press 01.01.2023
• Subjects: caputo's derivative; fixed point theorems; green's function; hyres-ulam stability; riemann-liouville integral
• ISSN: 2473-6988; 2473-6988
• DOI: 10.3934/math.2023514

In this manuscript, the main objective is to analyze the existence, uniqueness, (EU) and stability of positive solution for a general class of non-linear fractional differential equation (FDE) with fractional differential and fractional integral boundary conditions utilizing $ \phi_p $-Laplacian operator. To continue, we will apply Green's function to determine the suggested FDE's equivalent integral form. The Guo-Krasnosel'skii fixed point theorem and the properties of the $ p $-Laplacian operator are utilized to derive the existence results. Hyers-Ulam (HU) stability is additionally evaluated. Further, an application is presented to validate the effectiveness of the result.