Uniqueness and stability results of the abstract fractional spatial heterogeneous viral infection model

Khellaf Ould Melha; Medjahed Djilali; Vaijanath L. Chinchane; Asha B. Nale; Sabri T.M. Thabet; Imed Kedim

doi:10.1186/s13661-025-02077-9

Uniqueness and stability results of the abstract fractional spatial heterogeneous viral infection model

Khellaf Ould Melha
, Medjahed Djilali
, Vaijanath L. Chinchane
, Asha B. Nale
, Sabri T.M. Thabet
, Imed Kedim

Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

This paper proposes a general model of fractional spatial heterogeneouse viral infection. The resolvent operator’s method and a fixed point theorem are employed to establish the existence and uniqueness of mild solutions for abstract fractional spatial heterogeneous viral infection models. Additionally, the stability of Ulam–Hyers (UH) and Ulam–Hyers–Rassias (UHR) type for the solution of this model is studied. Examples of partial differential equations utilizing the Caputo–Fabrizio derivative are also presented.

Original language	English
Article number	82
Journal	Boundary Value Problems
Volume	2025
Issue number	1
DOIs	https://doi.org/10.1186/s13661-025-02077-9
State	Published - Dec 2025

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

SDG 3 Good Health and Well-being

Keywords

Abstract fractional differential equation
Caputo–Fabrizio fractional derivative
Resolvent operators
Spatial heterogeneous viral infection model
UH and UHR stability

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10.1186/s13661-025-02077-9

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abstract = "This paper proposes a general model of fractional spatial heterogeneouse viral infection. The resolvent operator{\textquoteright}s method and a fixed point theorem are employed to establish the existence and uniqueness of mild solutions for abstract fractional spatial heterogeneous viral infection models. Additionally, the stability of Ulam–Hyers (UH) and Ulam–Hyers–Rassias (UHR) type for the solution of this model is studied. Examples of partial differential equations utilizing the Caputo–Fabrizio derivative are also presented.",

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AU - Ould Melha, Khellaf

AU - Djilali, Medjahed

AU - Chinchane, Vaijanath L.

AU - Nale, Asha B.

AU - Thabet, Sabri T.M.

AU - Kedim, Imed

N1 - Publisher Copyright: © The Author(s) 2025.

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Y1 - 2025/12

N2 - This paper proposes a general model of fractional spatial heterogeneouse viral infection. The resolvent operator’s method and a fixed point theorem are employed to establish the existence and uniqueness of mild solutions for abstract fractional spatial heterogeneous viral infection models. Additionally, the stability of Ulam–Hyers (UH) and Ulam–Hyers–Rassias (UHR) type for the solution of this model is studied. Examples of partial differential equations utilizing the Caputo–Fabrizio derivative are also presented.

AB - This paper proposes a general model of fractional spatial heterogeneouse viral infection. The resolvent operator’s method and a fixed point theorem are employed to establish the existence and uniqueness of mild solutions for abstract fractional spatial heterogeneous viral infection models. Additionally, the stability of Ulam–Hyers (UH) and Ulam–Hyers–Rassias (UHR) type for the solution of this model is studied. Examples of partial differential equations utilizing the Caputo–Fabrizio derivative are also presented.

KW - Abstract fractional differential equation

KW - Caputo–Fabrizio fractional derivative

KW - Resolvent operators

KW - Spatial heterogeneous viral infection model

KW - UH and UHR stability

UR - https://www.scopus.com/pages/publications/105007533243

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DO - 10.1186/s13661-025-02077-9

M3 - Article

AN - SCOPUS:105007533243

SN - 1687-2762

VL - 2025

JO - Boundary Value Problems

JF - Boundary Value Problems

IS - 1

M1 - 82

ER -

Uniqueness and stability results of the abstract fractional spatial heterogeneous viral infection model

Abstract

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Keywords

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