An interesting quadratic fractional integral equation is investigated in this work via a generalized Mittag-Leffler (ML) function. The generalized ML–Hyers–Ulam stability is established in this investigation. We study both of the Hyers–Ulam stability (HUS) and ML–Hyers–Ulam–Rassias stability (ML-HURS) in detail for our proposed differential equation (DEq). Our proposed technique unifies various differential equations’ classes. Therefore, this technique can be further applied in future research works with applications to science and engineering.

Abstract:In this paper, we have presented and studied two types of the Mittag-Leffler-Hyers-Ulam stability of a fractional integral equation. We prove that the fractional order delay integral equation is Mittag-Leffler-Hyers-Ulam stable on a compact interval with respect to the Chebyshev and Bielecki norms by two notions.

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In this paper, we investigate some stability results concerning the k-cubic functional equation f (kx+y)+f (kx−y) = kf (x+y)+kf (x− y) + 2k(k 2 − 1)f (x) in the intuitionistic fuzzy n-normed spaces.Mathematics Subject Classification. Primary 46S40; Secondary 39B52, 39B82, 26E50, 46S50.