Fractional Differential Equations Computation and Modelling with Applications
Materialtyp:
ArtikelUtgivningsinformation: MDPI - Multidisciplinary Digital Publishing Institute 2025Beskrivning: 1 electronic resource (384 p.)Innehållstyp: - text
- computer
- online resource
- 9783725847419
- 9783725847426
- Reference, Information and Interdisciplinary subjects
- Research and information: general
- Mathematics and Science
- Adomian decomposition method
- Bessel equation
- Caputo fractional derivative
- Caputo fractional derivatives
- Caputo operator
- Elzaki transform
- FPDEs
- Fisher's equation
- FitzHugh–Nagumo equation
- H1-norm stability
- Helmholtz equation
- Hilfer fractional derivative
- Hyers–Ulam stability
- Hölder's inequality
- Laplace residual power series
- Legendre polynomials
- Lyapunov function
- Müntz–Legendre wavelets
- NL2 scheme
- NODE
- Neimark–Sacker bifurcation
- Schauder fixed-point theorem
- Shehu transform
- Toeplitz matrix method
- Yang transform
- adomian decomposition method
- basic reproduction number
- cardinal functions
- composite media
- constrained problem
- continuous dependence
- convergence
- dulac criteria
- error convergence
- existence and uniqueness
- fixed point theorem
- fixed-point theorem
- fractional differential equation
- fractional differential equations
- fractional integro-differential equations
- fractional model with vaccination
- fractional order
- fractional order infusion
- fractional order integro-differential RLC circuit
- fractional partial d
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In recent times, researchers across various fields have become interested in the topic of fractional calculus based on integrals and derivatives of fractional order. This area has numerous and widespread applications in fields of science and engineering, including wave and fluid dynamics, mathematical biology, financial systems, structural dynamics, robotics, and artificial intelligence, among others. Therefore, fractional models have become relevant in the context of phenomena with memory effects, in place of the conventional reliance on ordinary or partial differential equations. Fractional calculus offers superior tools for addressing time-dependent effects compared to integer-order calculus, which forms the foundation of most mathematical systems. As a result, fractional calculus is crucial to modeling real-life problems, and finding mathematical solutions is a great challenge in this regard.
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