In this paper, a new regularization term in the form of L1-norm based fractional gradient vector flow (LF-GGVF) is presented for the task of image denoising. A fractional order variational method is formulated, which is then utilized for estimating the proposed LF-GGVF. Overlapping group sparsity along with LF-GGVF is used as priors in image denoising optimization framework. The Riemann-Liouville derivative is used for approximating the fractional order derivatives present in the optimization framework. Its role in the framework helps in boosting the denoising performance. The numerical optimization is performed in an alternating manner using the well-known alternating direction method of multipliers (ADMM) and split Bregman techniques. The resulting system of linear equations is then solved using an efficient numerical scheme. A variety of simulated data that includes test images contaminated by additive white Gaussian noise are used for experimental validation. The results of numerical solutions obtained from experimental work demonstrate that the performance of the proposed approach in terms of noise suppression and edge preservation is better when compared with that of several other methods.