In this study, sinc-collocation method is introduced for solving Volterra-Fredholm integrodifferential equations of fractional order. Fractional derivative is described in the Caputo sense. Obtained results are given to literature as a new theorem. Some numerical examples are presented to demonstrate the theoretical results.

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In this paper, the cobweb model is reformulated in terms of fractional-order derivatives. In particular, we describe linear cobweb models in continuous time by using conformable fractional-order derivatives. Then, the general solutions as well as stability criteria for the proposed models are given. Moreover, the developed models are illustrated with some examples. KEYWORDScobweb model, conformable fractional derivative, fractional calculus 9010

In this study, a new model has been developed to monitor the contamination in connected three lakes. The model has been motivated by two biological models, i.e. cell compartment model and lake pollution model. Haar wavelet collocation method has been proposed for the numerical solutions of the model containing a system of three linear differential equations. In addition to the solutions of the system, convergence analysis has been briefly given for the proposed method. The contamination in each lake has been investigated by considering three different pollutant input cases, namely impulse imposed pollutant source, exponentially decaying imposed pollutant source, and periodic imposed pollutant source. Each case has been illustrated with a numerical example and results are compared with the exact ones. Regarding the results in each case it has been seen that, Haar wavelet collocation method is an efficient algorithm to monitor the contamination of a system of lakes problem.

In this study, the sinc collocation method is used to find an approximate solution of a system of differential equations of fractional order described in the Caputo sense. Some theorems are presented to prove the applicability of the proposed method to the system of fractional order differential equations. Some numerical examples are given to test the performance of the method. Approximate solutions are compared with exact solutions by examples. Some graphs and tables are presented to show the performance of the proposed method.