The implementation of a novel learning algorithm in artificial neural networks

This thesis introduces a novel learning algorithm called Karcı Fractional Artificial Neural Network (KarcıFANN), that builds upon Karcı fractional derivative approach. In KarcıFANN, a fractional derivative factor is incorporated alongside the classical (Newtonian) derivative of the error function with respect to the network weights. This factor is computed iteratively based on the current error and weight values and applied during the weight update process, allowing the learning dynamics to be largely governed by the model itself and minimizing external intervention. Within the scope of the thesis, experimental studies demonstrated the competitiveness of KarcıFANN against various optimization algorithms. Initially, the XOR problem was addressed in two experiments to assess the performance of KarcıFANN relative to ADAM, Momentum-based GD, and SGD. Subsequently, classification performance on the MNIST and Fashion-MNIST datasets was analyzed, comparing KarcıFANN with SGD. In addition, experiments on the Ginaprior_2 dataset examined the effect of different activation functions within KarcıFANN framework. Finally, comprehensive evaluations were conducted on three datasets of varying sizes using three- and four-layer models. The performance was assessed using MSE, CE, accuracy, precision, recall, and F1-score metrics.The findings indicate that KarcıFANN achieves faster and more efficient learning compared to classical ANNs. KarcıFANN effectively mitigates common challenges such as overfitting, underfitting, vanishing or exploding gradients, convergence to local minima, and oscillations. Moreover, consistent performance across multiple datasets demonstrates its generalization capability, suggesting that KarcıFANN is suitable for global modeling applications. Overall, these results position KarcıFANN as a competitive alternative to classical ANNs, offering enhanced convergence efficiency and adaptability across diverse data domains.