Non-Integer Calculus
The purpose of this reporting is to investigate the mathematical mechanics of a mass-point particleprojectiles with non-integer calculus. Nature presents volcanic rocks and tephra, sports' ball physics, as well as, ancient canon fire are relevant applications. The calculus explores fractional definitions of Caputo and Riemann-Louiville. This calculus has a historic origins beginning in a letter of to L'Hopital from Leibnitz in 1695 addressing a differential of fractional order. The report is written in five parts each utilizing a different calculus definition or approach. Problem formulations, solutions, and calculations are displayed for Caputo's approach in Part I, followed by a Riemann-Leibnitz formulations in Part II. Problems addressed include both cases, with and without drag forces, in a two-dimensional system. Part III presents a mathematical psychology model of learning kinetics. The model generalizes diffusion-kinetics with fractional calculus that utilizes a modified Riemann-Louiville definition and chain rule for a traveling wave solution. Part four addresses a fractional calculus model for vibrations with memory implementing a numerical discrete version for computation of the Riemann-Liouville fractional derivative. The fifth part presents a nonlinear acoustic wave with fractional loss operators. A transformed equation generalizing a Navier-Stokes Burgers equation with a polynomial multiplying the nonlinear term is solved with illustrative calculation. A system of fractional ordinary differential equations applied to an electrical circuit is presented in vector-matrix form and accompanying computation. Additional applications pertain to nonlinear enzyme kinetics formulation with matrices with solution, as well as, agglomeration dynamics.
"1134259637"
Non-Integer Calculus
The purpose of this reporting is to investigate the mathematical mechanics of a mass-point particleprojectiles with non-integer calculus. Nature presents volcanic rocks and tephra, sports' ball physics, as well as, ancient canon fire are relevant applications. The calculus explores fractional definitions of Caputo and Riemann-Louiville. This calculus has a historic origins beginning in a letter of to L'Hopital from Leibnitz in 1695 addressing a differential of fractional order. The report is written in five parts each utilizing a different calculus definition or approach. Problem formulations, solutions, and calculations are displayed for Caputo's approach in Part I, followed by a Riemann-Leibnitz formulations in Part II. Problems addressed include both cases, with and without drag forces, in a two-dimensional system. Part III presents a mathematical psychology model of learning kinetics. The model generalizes diffusion-kinetics with fractional calculus that utilizes a modified Riemann-Louiville definition and chain rule for a traveling wave solution. Part four addresses a fractional calculus model for vibrations with memory implementing a numerical discrete version for computation of the Riemann-Liouville fractional derivative. The fifth part presents a nonlinear acoustic wave with fractional loss operators. A transformed equation generalizing a Navier-Stokes Burgers equation with a polynomial multiplying the nonlinear term is solved with illustrative calculation. A system of fractional ordinary differential equations applied to an electrical circuit is presented in vector-matrix form and accompanying computation. Additional applications pertain to nonlinear enzyme kinetics formulation with matrices with solution, as well as, agglomeration dynamics.
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Non-Integer Calculus
146
Non-Integer Calculus
146Paperback
$32.00
32.0
In Stock
Product Details
| ISBN-13: | 9781078735964 |
|---|---|
| Publisher: | Barnes & Noble Press |
| Publication date: | 10/18/2019 |
| Pages: | 146 |
| Product dimensions: | 8.00(w) x 10.00(h) x 0.40(d) |
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