Fractional Differential Equations

Theoretical Aspects and Applications

Praveen Agarwal, Carlo Cattani, Shaher Momani, Praveen Agarwal, Carlo Cattani, Shaher Momani

• Publisher: Academic Press
• Year: 2024
• Print ISBN:
  9780443154232
• eBook ISBN:
  9780443154249
• Topic: Mathematics
• Subtopic: Applied Mathematics
• Index: Mathematics

Fractional Differential Equations: Theoretical Aspects and Applications presents the latest mathematical and conceptual developments in the field of Fractional Calculus and explores the scope of applications in research science and computational modelling. Fractional derivatives arise as a generalization of integer order derivatives and have a long history: their origin can be found in the work of G. W. Leibniz and L. Euler. Shortly after being introduced, the new theory turned out to be very attractive for many famous mathematicians and scientists, including P. S. Laplace, B. Riemann, J. Liouville, N. H. Abel, and J. B. J. Fourier, due to the numerous possibilities it offered for applications.Fractional Calculus, the field of mathematics dealing with operators of differentiation and integration of arbitrary real or even complex order, extends many of the modelling capabilities of conventional calculus and integer-order differential equations and finds its application in various scientific areas, such as physics, mechanics, engineering, economics, finance, biology, and chemistry, among others. However, many aspects from the theoretical and practical point of view have still to be developed in relation with models based on fractional operators. Efficient analytical and numerical methods have been developed but still need particular attention. Fractional Differential Equations: Theoretical Aspects and Applications delves into these methods and applied computational modelling techniques, including analysis of equations involving fractional derivatives, fractional derivatives and the wave equation, analysis of FDE on groups, direct and inverse problems, functional inequalities, and computational methods for FDEs in physics and engineering. Other modelling techniques and applications explored by the authors include general fractional derivatives involving the special functions in analysis, fractional derivatives with respect to another function in analysis, new fractional operators in real-world applications, fractional order dynamical systems, hidden attractors in complex systems, nonlinear dynamics and chaos in engineering applications, quantum chaos, and self-excited attractors. - Provides the most recent and up-to-date developments in the theory and scientific applications Fractional Differential Equations - Includes transportable computer source codes for readers in MATLAB, with code descriptions as it relates to the mathematical modelling and applications - Provides readers with a comprehensive foundational reference for this key topic in computational modeling, which is a mathematical underpinning for most areas of scientific and engineering research

Table of contents

• Fractional Differential Equations
• 1. Extension of the truncated M-fractional derivative linked to multivariate generalized Mittag-Leffler function demonstrating classical characteristics
• 2. A generalization of the Apostol-type Frobenius–Genocchi polynomials of level ι
• 3. Certain properties of generalized Mittag-Leffler operators
• 4. Differential operational techniques and applications
• 5. Some results on Wright function
• 6. Computational methods for the fractional differential equations in physics and engineering
• 7. A study on the properties of new generalized special functions, their integral transformations, and applications to fractional differential equations
• 8. Congruence between mild and classical solutions of generalized fractional impulsive evolution equation
• 9. Application of various methods to solve some fractional differential equations in different fields
• 10. Modeling capillary absorption in building materials with emphasis on the fourth root time law: time-fractional models, solutions, and analysis
• 11. Fuzzy fractional Caputo-type numerical scheme for solving fuzzy nonlinear equations
• 12. Approximate solutions of epidemic model of Zika virus
• 13. On the nonlocal boundary value problem for the coupled system
• 14. Solutions of nonlinear time fractional Klein–Gordon equations using composite fractional derivatives
• 15. Some generating functions for I -function
• 16. Approximate solution to the KdV equation in superthermal plasmas
• 17. Turátype inequalities for generalized fractional operators and special functions
• Index