methods of mathematical modelling fractional differential equations pdf hfxv

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==> methods of mathematical modelling fractional differential equations pdf <==

Methods of mathematical modeling involving fractional differential equations focus on extending traditional calculus to incorporate non-integer order derivatives, enabling a more accurate description of complex phenomena. These equations can capture memory and hereditary properties in various systems, making them suitable for applications in fields such as physics, engineering, biology, and finance. By delving into techniques like the Caputo and Riemann-Liouville derivatives, researchers can derive solutions and analyze behaviors of systems that exhibit anomalous diffusion or viscoelastic properties. The ultimate goal is to provide robust models that reflect real-world dynamics more faithfully than classical integer-order models. Additionally, numerical methods, such as finite difference and fractional finite element approaches, play a crucial role in solving these equations, allowing for practical implementations and further exploration of their implications in diverse scenarios.