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Fractional differential and integral operators with respect to a function = theory methods and applications /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Fractional differential and integral operators with respect to a function/ by Abdon Atangana, İlknur Koca.
其他題名:	theory methods and applications /
作者:	Atangana, Abdon.
其他作者:	Koca, İlknur.
出版者:	Singapore :Springer Nature Singapore : : 2025.,
面頁冊數:	xii, 412 p. :ill., digital ;24 cm.
內容註:	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.
Contained By:	Springer Nature eBook
標題:	Fractional differential equations. -
電子資源:	https://doi.org/10.1007/978-981-97-9951-0
ISBN:	9789819799510

Fractional differential and integral operators with respect to a function = theory methods and applications /
Atangana, Abdon.

Fractional differential and integral operators with respect to a functiontheory methods and applications /[electronic resource] :by Abdon Atangana, İlknur Koca. - Singapore :Springer Nature Singapore :2025. - xii, 412 p. :ill., digital ;24 cm. - Industrial and applied mathematics,2364-6845. - Industrial and applied mathematics..

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.

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.

ISBN: 9789819799510

Standard No.: 10.1007/978-981-97-9951-0doiSubjects--Topical Terms:

2184872
Fractional differential equations.

LC Class. No.: QA372

Dewey Class. No.: 515.35

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520 $a 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.
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