Some Contributions to Special Functions Using Fractional Calculus (Paperback)

Paperback. For three centuries, special functions and fractional calculus remained theoretical mathematical domains, but they have recently gained significant traction in engineering, science, and economics. This thesis explores their fundamental synergy, introducing new fractional derivative definitions using a two-parameter Mittag-Leffler kernel and applying them to Fourier's law and falling body problems. Additionally, the research presents a novel integral transform and a new special function derived from the Sturm-Liouville Equation, demonstrating their applications in solving high-dimensional Laplace and Schroedinger equations through analytical derivations and MATLAB simulations. This item is printed on demand. Shipping may be from our UK warehouse or from our Australian or US warehouses, depending on stock availability.