The ever-growing use of viscoelastic materials calls for the development of new theoretical models. Among these are materials that exhibit a liquid-to-solid phase transition. Models involving variable-order fractional operators are more suitable for predicting material behavior during such processes than classical models. In this diploma thesis, we present the derivation of such modified rheological models, constructed using variable-order fractional Caputo operators with partial memory-loss properties. We examine methods for solving the resulting equations and describe the implementation of our own numerical solver.
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