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

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), dependi...

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Published inBoundary value problems Vol. 2025; no. 1; pp. 113 - 14
Main Authors Sajid, Mohammad, Kalita, Hemanta, Zengin, Gülizar Gülenay, Wangwe, Lucas
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.12.2025
Hindawi Limited
SpringerOpen
Subjects
Analysis
Applications
Applied mathematics
Approximations and Expansions
Boundary value problems
Calculus
Comparison theorem
Difference and Functional Equations
Differential equations
Euclidean space
Fractal differential inequalities
Fractals
Independent variables
Initial value problem
Mathematics
Mathematics and Statistics
Maximal solution
Minimal solution
Ordinary Differential Equations
Partial Differential Equations
Recent Advances in Nonlinear Elliptic Partial Differential Equations: Theory
Minimal solution
Initial value problem
34A12
Differential equations
28A80
Fractal differential inequalities
Comparison theorem
Maximal solution
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Summary: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.
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ISSN:1687-2770
1687-2762
1687-2770
DOI:10.1186/s13661-025-02105-8