A TUTORIAL INTRODUCTION TO THE TWO-SCALE FRACTAL CALCULUS AND ITS APPLICATION TO THE FRACTAL ZHIBER–SHABAT OSCILLATOR

DOI10.1142/S0218348X21502686zbMath1506.35200OpenAlexW3201657229MaRDI QIDQ5082131

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Publication date: 15 June 2022

Published in: Fractals (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0218348x21502686

zbMATH Keywords

homotopy perturbation methodstability behaviorHe's frequency formulafractal nonlinear oscillatorZhiber-Shabat wave equation

Mathematics Subject Classification ID

Stability in context of PDEs (35B35) KdV equations (Korteweg-de Vries equations) (35Q53) Nonlinear ordinary differential equations and systems (34A34) Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05) Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Perturbations in context of PDEs (35B20) Fractals (28A80) Introductory exposition (textbooks, tutorial papers, etc.) pertaining to partial differential equations (35-01)

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Cites Work

• A gecko-like fractal receptor of a three-dimensional printing technology: a fractal oscillator
• Bifurcations of traveling wave solutions for Zhiber--Shabat equation
• Heat conduction in fractal tree-like branched networks
• New exact bounded travelling wave solutions for the Zhiber-Shabat equation
• Heat transfer and pressure drop in fractal tree-like microchannel nets
• Homotopy perturbation technique
• He's frequency formulation for nonlinear vibration of a porous foundation with fractal derivative
• Qualitative behavior and exact travelling wave solutions of the Zhiber-Shabat equation
• FRACTAL N/MEMS: FROM PULL-IN INSTABILITY TO PULL-IN STABILITY
• EQUIVALENT POWER-FORM REPRESENTATION OF THE FRACTAL TODA OSCILLATOR
• EFFECTS OF A CAVITY’S FRACTAL BOUNDARY ON THE FREE FRONT INTERFACE OF THE POLYMER FILLING STAGE
• Homotopy perturbation method with three expansions for Helmholtz-Fangzhu oscillator
• A REMARK ON WANG’S FRACTAL VARIATIONAL PRINCIPLE

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