With the growing digitization of financial services, fraudulent activities in online transactions are becoming increasingly sophisticated and widespread. An automated and intelligent financial transaction fraud detection system is necessary to properly detect and categorize fraudulent incidents in order to address this challenge. The majority of previous research has been on using binary classification to identify fraudulent transactions. Previous efforts were often hindered by class imbalance, inadequate feature selection, suboptimal prediction accuracy, and insufficient hyperparameter tuning. This paper suggests a hybrid deep learning framework for multi-class financial fraud detection that combines Convolutional Neural Network (CNN) and Closed-form Continuous-time (CfC) models in order to handle these problems. By analyzing transactional and behavioral characteristics, the model is intended to categorize fraud situations into distinct groups, including Phishing, Account Takeover (ATO), Card Skimming, and No Fraud. The proposed CfC-CNN model was not only trained but also tested on a large transaction augmented dataset that was enhanced with contextual characteristics. This work uses the IBM financial fraud dataset and considers 5 million transactions. This work investigated four classes such as phishing, ATO, card skimming, and no fraud. Label encoding was used as a preprocessing method for the contextual and category information. The dataset was refined for best performance by feature selection using Chi-Square and the random search method for hyper parameter tweaking. The proposed CfC-CNN model achieved at least .03 percent accuracy gain and .49 percent F1 score gain over the compared previous works.