Abstract
Abstract 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.
Highlights
Several types of integral equations (IEs) are considered very important in various functional analysis topics because of their essential role in engineering, physics, economics, and natural sciences
An interesting quadratic fractional integral equation is investigated in this work via a generalized Mittag-Le er (ML) function
We study both of the Hyers–Ulam stability (HUS) and ML– Hyers–Ulam–Rassias stability (ML-HURS) in detail for our proposed di erential equation (DEq)
Summary
Several types of integral equations (IEs) are considered very important in various functional analysis topics because of their essential role in engineering, physics, economics, and natural sciences. In the following year, that problem was investigated by Hyers for the Banach spaces (BaSps) case As a result, this particular stability is named as HUS. A generalized form of the Hyers’ theorem was studied by Rassias [4] in 1978 where the stability was investigated via unbounded Cauchy di erences. An extension of analysis to fractional di erential equations was investigated in many research works [7, 8]. There are equivalent types of di erential equations to quadratic fractional integral equation which acquire soliton solutions to have more e ective model equation than other related ones. A. Kaabar et al, A Generalized ML-Hyers-Ulam Stability of Quadratic Fractional Integral Equation.
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