Existence of maximal and minimal solutions initial value problem for the system of fractal differential equations

Sajid M., Kalita H., Zengin G. G., Wangwe L.

Boundary Value Problems, vol.2025, no.1, 2025 (SCI-Expanded, Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 2025 Issue: 1
  • Publication Date: 2025
  • Doi Number: 10.1186/s13661-025-02105-8
  • Journal Name: Boundary Value Problems
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, MathSciNet, Metadex, zbMATH, Directory of Open Access Journals, Civil Engineering Abstracts
  • Keywords: Comparison theorem, Differential equations, Fractal differential inequalities, Initial value problem, Maximal solution, Minimal solution
  • Uşak University Affiliated: Yes

Abstract

Differential equation refers to an equation that includes a function and its derivatives. These equations serve to model real-world situations where rates of change are significant. They are classified as either ordinary differential equations (ODEs) or partial differential equations (PDEs), depending on whether the unknown function is dependent on one or several independent variables, respectively. This paper presents a thorough investigation into fractal differential inequalities linked with an initial value fractal differential equation. It establishes the existence of a solution to this equation and demonstrates the convergence of both minimal and maximal solutions. Additionally, the paper introduces a comparative principle for evaluating solutions to the initial value problem associated with the fractal differential equation, ensuring a detailed and rigorous analysis of this subject.