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 in | Boundary value problems Vol. 2025; no. 1; pp. 113 - 14 |
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| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
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Cham
Springer International Publishing
01.12.2025
Hindawi Limited SpringerOpen |
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| 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. |
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| AbstractList | 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. 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. |
| ArticleNumber | 113 |
| Author | Sajid, Mohammad Kalita, Hemanta Wangwe, Lucas Zengin, Gülizar Gülenay |
| Author_xml | – sequence: 1 givenname: Mohammad surname: Sajid fullname: Sajid, Mohammad organization: Department of Mechanical Engineering, College of Engineering, Qassim University – sequence: 2 givenname: Hemanta surname: Kalita fullname: Kalita, Hemanta email: hemanta30kalita@gmail.com organization: Mathematics Division, School of Advanced Sciences and Languages, VIT Bhopal University – sequence: 3 givenname: Gülizar Gülenay surname: Zengin fullname: Zengin, Gülizar Gülenay organization: Department of Mathematics, Usak University – sequence: 4 givenname: Lucas surname: Wangwe fullname: Wangwe, Lucas organization: Department of Mathematics, Mbeya University of Science and Technology |
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| References | I. Podlubny (2105_CR14) 1999 2105_CR4 R. Figueroa (2105_CR6) 2012; 2012 A.K. Golmankhaneh (2105_CR8) 2023; 449 K.S. Miller (2105_CR12) 1993 A.K. Golmankhaneh (2105_CR7) 2024; 22 K. Falconer (2105_CR5) 2004 A. Parvate (2105_CR13) 2009; 17 B.B. Mandelbrot (2105_CR11) 1982 N. Kosmatov (2105_CR9) 2009; 70 P. Chen (2105_CR3) 2025; 14 A.O.H. Axelsson (2105_CR1) 1985; 45 N. Kosmatov (2105_CR10) 2009; 70 S.A. Burrell (2105_CR2) 2022; 199 |
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| SubjectTerms | 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 |
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| Title | Existence of maximal and minimal solutions initial value problem for the system of fractal differential equations |
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