Four Different Ulam-Type Stability for Implicit Second-Order Fractional Integro-Differential Equation with M-Point Boundary Conditions
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 (Hy...
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2025-01-01
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| author | Ilhem Nasrallah Rabiaa Aouafi Said Kouachi |
| author_facet | Ilhem Nasrallah Rabiaa Aouafi Said Kouachi |
| author_sort | Ilhem Nasrallah |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-7c173d9f912144b2b1327c8957711628 |
| institution | Kabale University |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-7c173d9f912144b2b1327c89577116282025-01-10T13:18:26ZengMDPI AGMathematics2227-73902025-01-0113115710.3390/math13010157Four Different Ulam-Type Stability for Implicit Second-Order Fractional Integro-Differential Equation with M-Point Boundary ConditionsIlhem Nasrallah0Rabiaa Aouafi1Said Kouachi2Laboratory E0560500 COSI, Department of Mathematics, Abbes Laghrour Khenchela University, Khenchela 40000, AlgeriaLaboratory E0560500 COSI, Department of Mathematics, Abbes Laghrour Khenchela University, Khenchela 40000, AlgeriaLaboratory E0560500 COSI, Department of Mathematics, Abbes Laghrour Khenchela University, Khenchela 40000, AlgeriaIn 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.https://www.mdpi.com/2227-7390/13/1/157fractional differential equationCaputo’s fractional derivativeUlam stabilitytwo-orderfixed point theorem |
| spellingShingle | Ilhem Nasrallah Rabiaa Aouafi Said Kouachi Four Different Ulam-Type Stability for Implicit Second-Order Fractional Integro-Differential Equation with M-Point Boundary Conditions Mathematics fractional differential equation Caputo’s fractional derivative Ulam stability two-order fixed point theorem |
| title | Four Different Ulam-Type Stability for Implicit Second-Order Fractional Integro-Differential Equation with M-Point Boundary Conditions |
| title_full | Four Different Ulam-Type Stability for Implicit Second-Order Fractional Integro-Differential Equation with M-Point Boundary Conditions |
| title_fullStr | Four Different Ulam-Type Stability for Implicit Second-Order Fractional Integro-Differential Equation with M-Point Boundary Conditions |
| title_full_unstemmed | Four Different Ulam-Type Stability for Implicit Second-Order Fractional Integro-Differential Equation with M-Point Boundary Conditions |
| title_short | Four Different Ulam-Type Stability for Implicit Second-Order Fractional Integro-Differential Equation with M-Point Boundary Conditions |
| title_sort | four different ulam type stability for implicit second order fractional integro differential equation with m point boundary conditions |
| topic | fractional differential equation Caputo’s fractional derivative Ulam stability two-order fixed point theorem |
| url | https://www.mdpi.com/2227-7390/13/1/157 |
| work_keys_str_mv | AT ilhemnasrallah fourdifferentulamtypestabilityforimplicitsecondorderfractionalintegrodifferentialequationwithmpointboundaryconditions AT rabiaaaouafi fourdifferentulamtypestabilityforimplicitsecondorderfractionalintegrodifferentialequationwithmpointboundaryconditions AT saidkouachi fourdifferentulamtypestabilityforimplicitsecondorderfractionalintegrodifferentialequationwithmpointboundaryconditions |