Fractal Differential Equations of 2<i>α</i>-Order
In this research paper, we provide a concise overview of fractal calculus applied to fractal sets. We introduce and solve a <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>2</mn><mi>α...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2024-11-01
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| Series: | Axioms |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2075-1680/13/11/786 |
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| Summary: | In this research paper, we provide a concise overview of fractal calculus applied to fractal sets. We introduce and solve a <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>2</mn><mi>α</mi></mrow></semantics></math></inline-formula>-order fractal differential equation with constant coefficients across different scenarios. We propose a uniqueness theorem for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>2</mn><mi>α</mi></mrow></semantics></math></inline-formula>-order fractal linear differential equations. We define the solution space as a vector space with non-integer orders. We establish precise conditions for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>2</mn><mi>α</mi></mrow></semantics></math></inline-formula>-order fractal linear differential equations and derive the corresponding fractal adjoint differential equation. |
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| ISSN: | 2075-1680 |