Abstract

AbstractVery recently, Atangana and Anum suggested a class of differential and integral operators with a constant fractional order and variable order fractal dimension. The idea was the extension of the concept of fractal-fractional differential and integral operators that was also suggested and applied in 2016. In this chapter, we consider a general Volterra equation with the new differential and integral operators. We present the condition under which the uniqueness and existence of the exact solutions can be obtained for three cases including power law, exponential decay law and the generalized Mittag-Leffler function. For each case, we present a numerical solution and error analysis. We present some illustrative examples.KeywordsFractal variable orderFractional orderNew Volterra equationNumerical analysis

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