To investigate a class of multi-singular pointwise defined fractional $ q $–integro-differential equation with applications

• Published in: AIMS mathematics Vol. 7; no. 5; pp. 7781 - 7816
• Main Authors: Samei, Mohammad Esmael, Karimi, Lotfollah, Kaabar, Mohammed K. A.
• Format: Journal Article
• Language: English
• Published: AIMS Press 01-01-2022
• Subjects: caputo q–derivation; integral boundary conditions; pointwise defined equations; singularity
• ISSN: 2473-6988; 2473-6988
• DOI: 10.3934/math.2022437

In the research work, we discuss a multi-singular pointwise defined fractional $ q $–integro-differential equation under some boundary conditions via the Riemann-Liouville $ q $–integral and Caputo fractional $ q $–derivatives. New existence results rely on the $ \alpha $-admissible map and fixed point theorem for $ \alpha $-$ \mathtt{ψ} $-contraction map. At the end, we present an example with application and some algorithms to illustrate the primary effects.