Existence, uniqueness and parameter perturbation analysis results of a fractional integro-differential boundary problem

• Autorzy: Zhang Nan , Zhang Lingling , Ngungu Mercy , Adeniji Adejimi , Addai Emmanuel

Identyfikatory

DOI

10.24425/bpasts.2023.145938

• Języki publikacji: EN

Abstrakty

EN

In the formulation, the existence, uniqueness and stability of solutions and parameter perturbation analysis to Riemann-Liouville fractional differential equations with integro-differential boundary conditions are discussed by the properties of Green’s function and cone theory. First, some theorems have been established from standard fixed point theorems in a proper Banach space to guarantee the existence and uniqueness of positive solution. Moreover, we discuss the Hyers-Ulam stability and parameter perturbation analysis, which examines the stability of solutions in the presence of small changes in the equation main parameters, that is, the derivative order η, the integral order β of the boundary condition, the boundary parameter ξ , and the boundary value τ. As an application, we present a concrete example to demonstrate the accuracy and usefulness of the proposed work. By using numerical simulation, we obtain the figure of unique solution and change trend figure of the unique solution with small disturbances to occur in different kinds of parameters.

Słowa kluczowe

EN

stability analysis; fractional differential equation; integro-differential boundary condition; existence; uniqueness; parameter perturbations

PL

istnienie; jednoznaczność; analiza stabilności; zaburzenia parametrów; ułamkowe równanie różniczkowe; warunek brzegowy całkowo-różniczkowy

• Wydawca: Polska Akademia Nauk, Wydział IV Nauk Technicznych
• Czasopismo: Bulletin of the Polish Academy of Sciences. Technical Sciences
• Rocznik: 2023
• Tom: Vol. 71, nr 4
• Strony: art. no. e145938
• Opis fizyczny: Bibliogr. 28 poz., rys.

Twórcy

autor

Zhang Nan

• College of Mathematics, Taiyuan University of Technology, 030024, TaiYuan, Shanxi, ChinaCollege of Mathematics, Taiyuan University of Technology, 030024, TaiYuan, Shanxi, China

autor

Zhang Lingling

• College of Mathematics, Taiyuan University of Technology, 030024, TaiYuan, Shanxi, China

• https://orcid.org/0000-0001-9532-6596

autor

Ngungu Mercy

• Human Sciences Research Council (HSRC), South Africa

autor

Adeniji Adejimi

• Tshwane university of Technology, South Africa

autor

Addai Emmanuel

• College of Mathematics, Taiyuan University of Technology, 030024, TaiYuan, Shanxi, China

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Uwagi

Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023).