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In the present manuscript, Crank Nicolson finite difference method is going to be applied to get the approximate solutions for the fractional Burgers equation. The fractional derivative used in this equation is going to be taken into consideration in the Caputo sense. The L1 type discretization formula is going to be applied to this equation. For checking the efficiency of proposed methods, the error norms L2 and L∞ have at the same time been calculated. Those newly got solutions using the presented method illustrate the easy usage and efficiency of the approach presented in this manuscript.

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The Çelikhan fluorite mineralization is concentrated in the thrust zone between the Pinarbasi Formation, which forms the hanging wall, and the Kalecik Limestone foot wall. Fluorite occurs as fracture fills in the thrust zone and as replacement of the foot wall. The wall rock alteration consists of calcite, barite, quartz and kaolinite. The total REE contents of the country rocks, especially the mica-and calc-schists of the Pinarbasi formation at 519 ppm, are higher than those of fluorites. The chondrite normalized REE patterns of country rock and fluorites display generally identical trends. However, fluorite patterns show positive Eu and negative Ce anomaly indicative of low temperature and high fo 2 conditions. Cross plots of the Tb/Ca-Tb/La, (La/Yb) n-(Tb/Yb) n and (La/Yb) n (Eu/Eu*) n ratios of the fluorites indicate deposition by low temperature hydrothermal waters. The REE and F were probably leached from the Pinarbasi Formation by the mineralizing solutions. The mineralizing fluids are probably meteoric and formation waters heated at depth along the thrust zone by the natural thermal gradient and/or formation waters heated and mobilized by thrusting.