Fractional and Multivariable Calculus: Model Building and Optimization

In this review of Fractional and Multivariable Calculus: Model Building and Optimization Problems readers will find a mathematically rigorous textbook aimed at researchers and advanced students who need a modern treatment of fractional calculus and multivariable methods for constructing models. The single biggest reason to buy is its focus on applying fractional integrals, fractional derivatives and multivariable techniques directly to deterministic and nondeterministic model building and optimization problems, distilled from a series of SERC lecture courses.

Key Features

• Lecture-based exposition: Material is drawn from five SERC Schools, which gives the book a structured, classroom-tested progression useful for self-study or course adoption.
• Fractional calculus foundation: The opening chapter explains fractional integrals and derivatives and shows how fractional differential equations are formulated and solved, providing tools for modeling anomalous dynamics.
• Multivariable methods: Coverage of multivariable calculus emphasizes techniques directly relevant to building and optimizing models across applied fields.
• Interdisciplinary orientation: Examples and motivation target mathematicians, statisticians, physicists, engineers and biological scientists seeking applicable modeling frameworks.
• Research-level depth: The text is comprehensive enough to serve as a reference for researchers while remaining usable by advanced undergraduates and graduate students.

Who It's For

Ideal readers include graduate students and researchers in mathematics, physics, engineering, statistics and mathematical biology who need a rigorous treatment of fractional calculus and multivariable optimization to build deterministic or nondeterministic models. The book is especially useful for those preparing to apply fractional differential equations in applied research.

Who should look elsewhere are beginners seeking an elementary introduction without advanced prerequisites, or practitioners who want a brief applied handbook with many worked engineering examples rather than a lecture-style, theory-forward presentation.

Pros & Cons

Pros

• Clear, lecture-tested organization makes it straightforward to follow as a course text or independent study resource.
• Strong, focused treatment of fractional differential equations that connects theory to model building.
• Broad applicability across disciplines supports cross-field modeling and optimization work.

Cons

• Presentation is research-level and assumes substantial mathematical background, so it is not a gentle primer for novices.

Specifications

Title	Fractional and Multivariable Calculus: Model Building and Optimization Problems
Series	Springer Optimization and Its Applications, 122
Authors	A.M. Mathai, H.J. Haubold
Scope	Fractional calculus, multivariable calculus, model building, optimization
Audience	Researchers, advanced undergraduates, graduate students
Origin	Based on lectures at five SERC Schools (2008-2012)

Our Verdict

This book is a strong, academically rigorous choice for readers who need a thorough theoretical foundation in fractional calculus and multivariable optimization for model building. It represents good value for advanced students and researchers who will use the methods in applied or theoretical projects, but casual readers or beginners should choose a more elementary introduction first.

Frequently Asked Questions

Does this book teach fractional differential equation solution methods?
Yes. The opening chapter introduces fractional integrals, fractional derivatives and methods for solving fractional differential equations.

Is this suitable for undergraduate coursework?
It is suitable for advanced undergraduates with strong prerequisites, but it is primarily aimed at graduate students and researchers.

Does the book include applied examples for other fields?
Yes. The text emphasizes interdisciplinary applications and model-building examples relevant to physics, engineering, statistics and biological sciences.