Four Different Ulam-Type Stability for Implicit Second-Order Fractional Integro-Differential Equation with M-Point Boundary Conditions

Ilhem Nasrallah (), Rabiaa Aouafi and Said Kouachi
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Ilhem Nasrallah: Laboratory E0560500 COSI, Department of Mathematics, Abbes Laghrour Khenchela University, Khenchela 40000, Algeria
Rabiaa Aouafi: Laboratory E0560500 COSI, Department of Mathematics, Abbes Laghrour Khenchela University, Khenchela 40000, Algeria
Said Kouachi: Laboratory E0560500 COSI, Department of Mathematics, Abbes Laghrour Khenchela University, Khenchela 40000, Algeria

Mathematics, 2025, vol. 13, issue 1, 1-12

Abstract: In this paper, we discuss the existence and uniqueness of a solution for the implicit two-order fractional integro-differential equation with m-point boundary conditions by applying the Banach fixed point theorem. Moreover, in the paper we establish the four different varieties of Ulam stability (Hyers–Ulam stability, generalized Hyers–Ulam stability, Hyers–Ulam-Rassias stability, and generalized Hyers–Ulam–Rassias stability) for the given problem.

Keywords: fractional differential equation; Caputo’s fractional derivative; Ulam stability; two-order; fixed point theorem (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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