How can graph theory be used to study fractional differential equations?
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Graph theory is used to study fractional differential equations by analyzing the interconnections between chemical systems. Researchers have utilized star graphs to examine the space of possible solutions for boundary-value problems in fractional differential equations . Star graphs are chosen because they have a central node connected to other nodes but not to itself, which is essential for the technique used in studying these equations. Additionally, the concept of other chemical graphs such as neopentane and ethane graphs has been introduced to expand the scope of the method . Theorems such as the Schaefer and Krasnoselskii fixed point theorems are employed to determine the existence and uniqueness of solutions to the presented boundary value problems . These approaches provide insights into the solutions of fractional differential equations and contribute to the field of mathematical chemistry and chemical graph theory.
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| Papers (4) | Insight |
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| Graph theory is used in the paper to develop a novel graph-operational matrix method for solving multidelay fractional differential equations with variable coefficients. | |
9 Citations | Graph theory can be used to study fractional differential equations by representing the equations on graphs and using graph properties to analyze the existence and uniqueness of solutions. |
3 Citations | Graph theory is used in the paper to develop a new approach called the clique polynomial method (CPM) for solving fractional partial differential equations (FPDE). |
8 Citations | The paper uses graph theory to study fractional boundary value problems by introducing the concept of an octane graph, which is influenced by the structure of the chemical substance octane. |
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