The Fractional-order model of fin problem in the presence of a temperature-dependent rate of internal heat generation in fin material has been studied in the proposed paper. Fractional-order Legendre functions (F-OLFs) with the Galerkin approach has been used to compute the result of the proposed fin problem. The exact solution is also calculated in a particular case of our fractional-order fin problem. The proposed fin problem has been presented in the non-dimension form. Temperature distribution in the straight fin is calculated for different values of used variables or parameters along space coordinate. The impact of different parameters such as fractional order, fin parameter, internal heat generation, generation number, etc. on the temperature profile in the fin is described in detail. The cooling process is faster in fractional order fin problem than the integer-order.

在翅片材料中，研究了翅片问题的分数阶模型，该翅片问题存在温度依赖的内部发热速率。带有Galerkin方法的分数阶Legendre函数（F-OLF）已用于计算所提出的鳍问题的结果。在分数阶鳍问题的特定情况下，也可以计算出精确解。拟议的翅片问题已以无量纲形式提出。对于沿空间坐标使用的变量或参数的不同值，计算直翅片中的温度分布。详细描述了不同参数（例如分数阶，散热片参数，内部发热量，发热量等）对散热片中温度曲线的影响。