Using the decomposition method to solve the fractional order temperature distribution equation: A new approach

Due to its importance in science, finding both exact and approximate solutions to fractional partial differential equations with boundary conditions is important for the research community. The natural decomposition method (NDM), which is based on the natural transformation method (NTM) and the Adom...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Mathematical methods in the applied sciences 2023-09, Vol.46 (13), p.14321-14339
Hauptverfasser: Rawashdeh, Mahmoud S., Obeidat, Nazek A., Ababneh, Omar M.
Format: Artikel
Sprache:eng
Schlagworte:
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung:Due to its importance in science, finding both exact and approximate solutions to fractional partial differential equations with boundary conditions is important for the research community. The natural decomposition method (NDM), which is based on the natural transformation method (NTM) and the Adomian decomposition method, is modified in this study to produce exact and approximate solutions for boundary value problems (BVPs) of partial differential equations (PDEs) with fractional coefficients. In addition, we present an exact solution to the temperature distribution in a slab constructed of materials with variable thermal conductivity's combined convection–radiation lumped system. We present these findings as numerical tables and graphs that show the convergence and stability rates. The study demonstrates that this approach is effective since it is simple to apply and produces reliable findings. We are the first to use this approach for such applications, as far as we are aware. Additionally, this method is applicable to a sizable class of BVPs for ordinary differential equations (ODEs) and PDEs.
ISSN:0170-4214
1099-1476
DOI:10.1002/mma.9321