New Challenges Arising in Engineering Problems with Fractional and Integer Order
Baskonus, Haci Mehmet
New Challenges Arising in Engineering Problems with Fractional and Integer Order - Basel, Switzerland MDPI - Multidisciplinary Digital Publishing Institute 2021 - 1 electronic resource (182 p.)
Open Access
Mathematical models have been frequently studied in recent decades, in order to obtain the deeper properties of real-world problems. In particular, if these problems, such as finance, soliton theory and health problems, as well as problems arising in applied science and so on, affect humans from all over the world, studying such problems is inevitable. In this sense, the first step in understanding such problems is the mathematical forms. This comes from modeling events observed in various fields of science, such as physics, chemistry, mechanics, electricity, biology, economy, mathematical applications, and control theory. Moreover, research done involving fractional ordinary or partial differential equations and other relevant topics relating to integer order have attracted the attention of experts from all over the world. Various methods have been presented and developed to solve such models numerically and analytically. Extracted results are generally in the form of numerical solutions, analytical solutions, approximate solutions and periodic properties. With the help of newly developed computational systems, experts have investigated and modeled such problems. Moreover, their graphical simulations have also been presented in the literature. Their graphical simulations, such as 2D, 3D and contour figures, have also been investigated to obtain more and deeper properties of the real world problem.
Creative Commons
English
books978-3-0365-1969-2 9783036519685 9783036519692
10.3390/books978-3-0365-1969-2 doi
Technology: general issues
fractional kinetic equation Riemann-Liouville fractional integral operator incomplete I-functions Laplace transform fractional differential equations fractional generalized biologic population Sumudu transform Adomian decomposition method Caputo fractional derivative operator theory time scales integral inequalities Burgers' equation reproducing kernel method error estimate Dirichlet and Neumann boundary conditions Caputo derivative Laplace transforms constant proportional Caputo derivative modeling Volterra-type fractional integro-differential equation Hilfer fractional derivative Lorenzo-Hartely function generalized Lauricella confluent hypergeometric function Elazki transform caputo fractional derivative predator-prey model harvesting rate stability analysis equilibrium point implicit discretization numerical scheme the (m + 1/G')-expansion method the (2+1)-dimensional hyperbolic nonlinear Schrödinger equation periodic and singular complex wave solutions traveling waves solutions chaotic finance fractional calculus Atangana-Baleanu derivative uniqueness of the solution fixed point theory shifted Legendre polynomials variable coefficient three-point boundary value problem modified alpha equation Bernoulli sub-equation function method rational function solution complex solution contour surface variable exponent fractional integral maximal operator n/a
New Challenges Arising in Engineering Problems with Fractional and Integer Order - Basel, Switzerland MDPI - Multidisciplinary Digital Publishing Institute 2021 - 1 electronic resource (182 p.)
Open Access
Mathematical models have been frequently studied in recent decades, in order to obtain the deeper properties of real-world problems. In particular, if these problems, such as finance, soliton theory and health problems, as well as problems arising in applied science and so on, affect humans from all over the world, studying such problems is inevitable. In this sense, the first step in understanding such problems is the mathematical forms. This comes from modeling events observed in various fields of science, such as physics, chemistry, mechanics, electricity, biology, economy, mathematical applications, and control theory. Moreover, research done involving fractional ordinary or partial differential equations and other relevant topics relating to integer order have attracted the attention of experts from all over the world. Various methods have been presented and developed to solve such models numerically and analytically. Extracted results are generally in the form of numerical solutions, analytical solutions, approximate solutions and periodic properties. With the help of newly developed computational systems, experts have investigated and modeled such problems. Moreover, their graphical simulations have also been presented in the literature. Their graphical simulations, such as 2D, 3D and contour figures, have also been investigated to obtain more and deeper properties of the real world problem.
Creative Commons
English
books978-3-0365-1969-2 9783036519685 9783036519692
10.3390/books978-3-0365-1969-2 doi
Technology: general issues
fractional kinetic equation Riemann-Liouville fractional integral operator incomplete I-functions Laplace transform fractional differential equations fractional generalized biologic population Sumudu transform Adomian decomposition method Caputo fractional derivative operator theory time scales integral inequalities Burgers' equation reproducing kernel method error estimate Dirichlet and Neumann boundary conditions Caputo derivative Laplace transforms constant proportional Caputo derivative modeling Volterra-type fractional integro-differential equation Hilfer fractional derivative Lorenzo-Hartely function generalized Lauricella confluent hypergeometric function Elazki transform caputo fractional derivative predator-prey model harvesting rate stability analysis equilibrium point implicit discretization numerical scheme the (m + 1/G')-expansion method the (2+1)-dimensional hyperbolic nonlinear Schrödinger equation periodic and singular complex wave solutions traveling waves solutions chaotic finance fractional calculus Atangana-Baleanu derivative uniqueness of the solution fixed point theory shifted Legendre polynomials variable coefficient three-point boundary value problem modified alpha equation Bernoulli sub-equation function method rational function solution complex solution contour surface variable exponent fractional integral maximal operator n/a