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New Challenges Arising in Engineering Problems with Fractional and Integer Order
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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.
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Keywords
- Adomian decomposition method
- Atangana-Baleanu derivative
- Bernoulli sub-equation function method
- Burgers’ equation
- Caputo derivative
- Caputo fractional derivative
- chaotic finance
- complex solution
- constant proportional Caputo derivative
- contour surface
- Dirichlet and Neumann boundary conditions
- Elazki transform
- equilibrium point
- error estimate
- fixed point theory
- Fractional calculus
- fractional differential equations
- fractional generalized biologic population
- fractional integral
- fractional kinetic equation
- generalized Lauricella confluent hypergeometric function
- harvesting rate
- Hilfer fractional derivative
- implicit discretization numerical scheme
- incomplete I-functions
- integral inequalities
- Laplace transform
- laplace transforms
- Lorenzo-Hartely function
- maximal operator
- modeling
- modified alpha equation
- n/a
- Operator theory
- periodic and singular complex wave solutions
- predator–prey model
- rational function solution
- reproducing kernel method
- Riemann–Liouville fractional integral operator
- shifted Legendre polynomials
- stability analysis
- Sumudu transform
- Technology, engineering, agriculture
- Technology: general issues
- the (2+1)-dimensional hyperbolic nonlinear Schrödinger equation
- the (m + 1/G′)-expansion method
- three-point boundary value problem
- time scales
- traveling waves solutions
- uniqueness of the solution
- variable coefficient
- variable exponent
- Volterra-type fractional integro-differential equation
Links
DOI: 10.3390/books978-3-0365-1969-2Editions