Discrete Fractional Calculus and Fractional Difference Equations (SpringerBriefs in Mathematics)

✍ Scribed by Rui A. C. Ferreira

Publisher: Springer
Year: 2022
Tongue: English
Leaves: 95
Category: Library

No coin nor oath required. For personal study only.

✦ Synopsis

This brief aims to merge the theories of fractional calculus and discrete calculus in a concise but comprehensive manner. It is designed for graduate students, but will be useful for any researcher interested in the theory of discrete fractional calculus and fractional difference equations.

✦ Table of Contents

Preface
Contents
1 Discrete Calculus
1.1 The Difference and Summation Operators
1.2 Discrete Exponential Function
1.3 Exercises
2 Discrete Fractional Calculus
2.1 Motivation
2.2 The Fractional Sums and Differences
2.3 Power Rules
2.4 Composition Rules
2.5 Fractional Leibniz Formula
2.6 A Digression into Physics: A Novel Entropic Functional
2.7 Exercises
3 Fractional Difference Equations
3.1 Linear Difference Equations
3.1.1 Two Inequalities
3.1.2 Asymptotic Behavior
3.1.3 Stability
3.2 Nonlinear Difference Equations: Influence of Perturbed Data
3.3 Boundary Value Problems
3.4 Exercises
4 Calculus of Variations
4.1 Necessary Conditions
4.2 Natural Boundary Conditions
4.3 A Sufficient Condition
4.4 Exercises
References
Index

📜 SIMILAR VOLUMES

Functional Fractional Calculus

📁 Functional Fractional Calculus

✍ Shantanu Das (auth.) 📂 Library 📅 2011 🏛 Springer-Verlag Berlin Heidelberg 🌐 English

When a new extraordinary and outstanding theory is stated, it has to face criticism and skeptism, because it is beyond the usual concept. The fractional calculus though not new, was not discussed or developed for a long time, particularly for lack of its application to real life problems. It i

Functional Fractional Calculus

📁 Functional Fractional Calculus

✍ Shantanu Das (auth.) 📂 Library 📅 2011 🏛 Springer-Verlag Berlin Heidelberg 🌐 English

Functional Fractional Calculus

📁 Functional Fractional Calculus

✍ Shantanu Das 📂 Library 📅 2011 🏛 Springer 🌐 English

When a new extraordinary and outstanding theory is stated, it has to face criticism and skeptism, because it is beyond the usual concept. The fractional calculus though not new, was not discussed or developed for a long time, particularly for lack of its application to real life problems. I

Discrete Hamiltonian Systems: Difference

📁 Discrete Hamiltonian Systems: Difference Equations, Continued Fractions, and Riccati Equations

✍ Calvin D. Ahlbrandt, Allan C. Peterson (auth.) 📂 Library 📅 1996 🏛 Springer US 🌐 English

This book should be accessible to students who have had a first course in matrix theory. The existence and uniqueness theorem of Chapter 4 requires the implicit function theorem, but we give a self-contained constructive proof ofthat theorem. The reader willing to accept the implicit function the

Advances in Special Functions of Fractio

📁 Advances in Special Functions of Fractional Calculus: Special Functions in Fractional Calculus and Their Applications in Engineering

✍ Praveen Agarwal, Shilpi Jain 📂 Library 📅 2023 🏛 Bentham Science Publishers 🌐 English

In recent years, special functions have been developed and applied in a variety of fields, such as combinatorics, astronomy, applied mathematics, physics, and engineering due to their remarkable properties. This volume expands our understanding of special functions by highlighting recen

Advances in Special Functions of Fractio

📁 Advances in Special Functions of Fractional Calculus: Special Functions in Fractional Calculus and Their Applications in Engineering

✍ Praveen Agarwal, Shilpi Jain 📂 Library 📅 2023 🏛 Bentham Books 🌐 English