Electronic Journal of Differential Equations, 
Vol. 2020 (2020), No. 132, pp. 1-16.

Title: Existence and stability for fractional order pantograph equations with nonlocal conditions
       
Authors: Israr Ahmad (Univ. of Malakand, Chakdara, Khyber Pakhtunkhwa, Pakistan)
         Juan Jose Nieto (Univ. de Santiago de Compostela, Spain)
         Ghaus ur Rahman (Univ. of Swat, Khyber Pakhtunkhwa, Pakistan)
         Kamal Shah (Univ. of Malakand, Chakdara, Khyber Pakhtunkhwa, Pakistan)

Abstract:
In this article we study the a coupled system of fractional pantograph differential
 equations (FPDEs). Using degree theory, we state necessary conditions for the existence of
 solutions to a coupled system of fractional partial differential equations with non-local
 boundary conditions. Also using tools from non-linear analysis, we establish some stability
 results. We illustrate our theoretical results with a test problem.

Submitted December 11, 2019. Published December 26, 2020.
Math Subject Classifications: 26A33, 34A08, 35R11.
Key Words: Coupled system; non-local boundary conditions; stability theory;
           pantograph equation.