Fractional Differential and Integral Operators with Respect to a Function : Theory Methods and Applications / by Abdon Atangana, İlknur Koca.

Format:

Book

Author/Creator:

Atangana, Abdon.

Contributor:

Koca, İlknur.

Series:

Industrial and Applied Mathematics, 2364-6845

Language:

English

Subjects (All):

Differential equations.

Mathematical analysis.

Differential Equations.

Analysis.

Local Subjects:

Differential Equations.

Analysis.

Physical Description:

1 online resource (441 pages)

Edition:

1st ed. 2025.

Place of Publication:

Singapore : Springer Nature Singapore : Imprint: Springer, 2025.

Summary:

This book explores the fundamental concepts of derivatives and integrals in calculus, extending their classical definitions to more advanced forms such as fractional derivatives and integrals. The derivative, which measures a function's rate of change, is paired with its counterpart, the integral, used for calculating areas and volumes. Together, they form the backbone of differential and integral equations, widely applied in science, technology, and engineering. However, discrepancies between mathematical models and experimental data led to the development of extended integral forms, such as the Riemann–Stieltjes integral and fractional integrals, which integrate functions with respect to another function or involve convolutions with kernels. These extensions also gave rise to new types of derivatives, leading to fractional derivatives and integrals with respect to another function. While there has been limited theoretical exploration in recent years, this book aims to bridge that gap. It provides a comprehensive theoretical framework covering inequalities, nonlinear ordinary differential equations, numerical approximations, and their applications. Additionally, the book delves into the existence and uniqueness of solutions for nonlinear ordinary differential equations involving these advanced derivatives, as well as the development of numerical techniques for solving them.

Contents:

History of differential and integral calculus.-Global derivatives, definitions and properties

Integral operators, definitions and properties

Inequalities related to global fractional derivatives

Inequalities associated to Integrals

Existence and Uniqueness of IVP with global differentiation on via Picard iteration

Existence and uniqueness via Carathéodory approach

Existence and uniqueness analysis of nonlocal global differential equations with expectation approach

Chaplygin’s method for global differential equations

Numerical analysis of IVP with classical global derivative.-Numerical analysis of IVP with Riemann-Liouville global derivative

Numerical analysis of IVP with Caputo-Fabrizio global derivative

Numerical analysis of IVP with Atangana-Baleanu global derivative

Examples and applications of global fractional differential equations.

Notes:

Description based on publisher supplied metadata and other sources.

ISBN:

9789819799510

9819799511

OCLC:

1499721620