Establishing the existence of Hilfer fractional pantograph equations with impulses

Authors : Sugumaran Harikrishnan, Rabha Ibrahim, Kuppusamy Kanagarajan

Pages : 36-42

Doi:10.33401/fujma.406651

View : 18 | Download : 12

Publication Date : 2018-06-30

Article Type : Research

Abstract :In [1], the authors established the existence of a class of fractional differential equations of a complex order. In this note, we derive some sufficient conditions for the existence of solutions to a class of Hilfer fractional pantograph equations with impulsive effect. Further, using the techniques of nonlinear functional analysis, we establish appropriate conditions and results to discuss various kinds of Ulam-Hyers stability.
Keywords : Pantograph equation, Impulsive condition, Fixed point stability