On a new structure of multi-term Hilfer fractional impulsive neutral Levin-Nohel integrodifferential system with variable time delay
Thabet Abdeljawad, Sabri T.M. Thabet, Imed Kedim, Miguel Vivas-Cortez
- Facultad de Ciencias Exactas y Naturales
Resumen
The Levin-Nohel equations play key roles in the interpretation of real phenomena and have interesting applications in engineering and science areas, such as mathematical physics, mathematical biology, image processing, and numerical analyses. This article investigates a new structure for the delay neutral Levin-Nohel integrodifferential (NLNID) system via a Hilfer fractional derivative and is supplemented by initial and instantaneous impulse conditions. A fractional integral equation corresponding to the proposed system is derived and used to prove the existence and uniqueness of the solution with the help of the Banach contraction principle. Additionally, the Ulam-Hyers-MittagLeffler (UHML) stability is studied by utilizing the generalized Gronwall’s inequality and nonlinear analysis issues. As a consequence, the Ulam-Hyers (UH) stability and generalized UH are also deduced. Furthermore, the Riemann-Liouville (R.L.) and Caputo fractional versions of the proposed system are discussed. Finally, numerical applications supported with tables and graphics are provided to test the exactitude of the findings.
Idioma original Inglés Páginas (desde-hasta) 7372-7395 Número de páginas 24 Publicación AIMS Mathematics Volumen 9 N.º 3 Estado Publicada - 2024
The Levin-Nohel equations play key roles in the interpretation of real phenomena and have interesting applications in engineering and science areas, such as mathematical physics, mathematical biology, image processing, and numerical analyses. This article investigates a new structure for the delay neutral Levin-Nohel integrodifferential (NLNID) system via a Hilfer fractional derivative and is supplemented by initial and instantaneous impulse conditions. A fractional integral equation corresponding to the proposed system is derived and used to prove the existence and uniqueness of the solution with the help of the Banach contraction principle. Additionally, the Ulam-Hyers-MittagLeffler (UHML) stability is studied by utilizing the generalized Gronwall’s inequality and nonlinear analysis issues. As a consequence, the Ulam-Hyers (UH) stability and generalized UH are also deduced. Furthermore, the Riemann-Liouville (R.L.) and Caputo fractional versions of the proposed system are discussed. Finally, numerical applications supported with tables and graphics are provided to test the exactitude of the findings.
| Idioma original | Inglés |
|---|---|
| Páginas (desde-hasta) | 7372-7395 |
| Número de páginas | 24 |
| Publicación | AIMS Mathematics |
| Volumen | 9 |
| N.º | 3 |
| Estado | Publicada - 2024 |
Nota bibliográfica
Publisher Copyright:
© 2024 the Author(s), licensee AIMS Press.
© 2024 the Author(s), licensee AIMS Press.
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