Recent Trends in Fractional Calculus and Its Applications

Praveen Agarwal,Luis Vázquez Martínez,Ervin K. Lenzi

• Publisher: Academic Press
• Year: 2024
• ISBN:
  9780443185069
• Topic: Sciences biologiques
• Subtopic: Biologie moléculaire

Recent Trends in Fractional Calculus and Its Applications addresses the answer to this very basic question: "Why is Fractional Calculus important?" Until recent times, Fractional Calculus was considered as a rather esoteric mathematical theory without applications, but in the last few decades there has been an explosion of research activities on the application of Fractional Calculus to very diverse scientific fields ranging from the physics of diffusion and advection phenomena, to control systems to finance and economics. An important part of mathematical modelling of objects and processes is a description of their dynamics.The term Fractional Calculus is more than 300 years old. It is a generalization of the ordinary differentiation and integration to noninteger (arbitrary) order. The subject is as old as the calculus of differentiation and goes back to times when Leibniz, Gauss, and Newton invented this kind of calculation. Several mathematicians contributed to this subject over the years. People like Liouville, Riemann, and Weyl made major contributions to the theory of Fractional Calculus. In recent decades the field of Fractional Calculus has attracted the interest of researchers in several areas, including mathematics, physics, chemistry, engineering, finance, and social sciences.

• Provides the most recent and up-to-date developments in the Fractional Calculus and its application areas
• Presents pre-preparation ideas to help researchers/scientists/clinicians face the new challenges in the application of fractional differential equations
• Helps researchers and scientists understand the importance of the Fractional Calculus to solve many problems in Biomedical Engineering and applied sciences

Table of contents

• Cover image
• Title page
• Table of Contents
• Copyright
• List of contributors
• 1: On generalized Dirichlet averages and fractional calculus
• 2: Generalizations of some important fractional integral inequalities by using a parameter
• 3: Elzaki transform of pathway fractional integral formulae involving extended k-hypergeometric functions
• 4: Application of fractional-order Fibonacci wavelets to solve variable-order fractional partial differential equations
• 5: Optimization of the approximate solution of the fractional squeezing flow between two infinite plates
• 6: Multi-parameter generalized fractional operators and their integral transforms
• 7: A constructive approach to the fractional Zakharov–Kuznetsov equations of weak nonlinear acoustic ion waves in plasma
• 8: Integral formula for matrix factorizations of Helmholtz equation
• 9: Cauchy problem for matrix factorizations of Helmholtz equation on a plane
• 10: The Cauchy problem for matrix factorizations of Helmholtz equation in space
• 11: Modified Newton successive over-relaxation for solving Caputo fractional porous medium equations
• 12: Fractional calculi on time scales: differentiation and integration of a function with respect to another function
• 13: Effective strategies to reduce transmission of certain diseases based on their fractional optimal control problems
• 14: Fractional Caputo-type simultaneous scheme for finding all polynomial roots
• 15: Application of modified homotopy analysis transform method to fractional modified Kawahara equation
• Index