Summary: A Fractional Derivative Approach to Fractional Diffusion Equations
The study, co-authored by Fullbright, delves into the application of fractional differential equations in modeling complex systems, particularly focusing on diffusion processes. The research introduces a new method to solve fractional diffusion equations with Caputo derivatives, developing a framework to address initial value problems. The author employs the Laplace transform and the SAKOROWSKI method, exploring the existence and uniqueness of solutions, highlighting the importance of Lipschitz continuity in ensuring the well-posedness of these equations. The conclusion establishes a general framework for solving fractional diffusion equations using a one-parameter family of operators, contributing to the field’s understanding of fractional calculus’s practical applications in various scientific and engineering disciplines.
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