On Ulam’s type stability criteria for fractional integral equations including Hadamard type singular kernel

Abstract

In this paper, we deal with the Hyers-Ulam-Rassias (HUR) and Hyers-Ulam (HU) stability of Hadamard type fractional integral equations on compact intervals. The stability conditions are developed using a new generalized metric (GM) definition and the fixed point technique by motivating Wang and Lin Ulam's type stability of Hadamard type fractional integral equations. Filomat 2014; 28(7): 1323-1331. Moreover, our approach is efficient and ease in use than to the previously studied approaches. Finally, we give two examples to explain our main results.

Hyers-Ulam stability of a certain Fredholm integral equation

“…After that Aoki [2], Bourgin [4] and Rassias [24] have generalized the Hyers result. These days the Hyers-Ulam stability for different functional equations was proved by many mathematicians (see [9,14,25,32]). A generalization Ulam problem was recently proposed by replacing functional equations with differential equations.…”