Boundary Value Problems and Applications for Mixed Type Loaded PDEs

1. Auflage 2026
ISBN: 978-1-041-35228-0
Verlag: Taylor & Francis

Buch, Englisch, 352 Seiten, Format (B × H): 156 mm x 234 mm

This book is devoted to the analytical study of boundary value problems for third-order parabolic–hyperbolic equations containing nonlocal and fractional loaded terms. It develops a unified analytical framework for the investigation of local and nonlocal formulations, bringing together classical partial differential equation theory and fractional calculus. Particular attention is paid to the solvability theory of Tricomi-, Gellerstedt-, and Darboux-type problems, including the establishment of existence and uniqueness theorems and the derivation of explicit solution representations.

The book extends traditional models through the incorporation of Riemann–Liouville fractional integro-differential operators and explores the connections between local and nonlocal formulations by means of integral transformation techniques and inverse problem methods. Special emphasis is placed on reduction procedures that transform third-order equations into lower-order systems, facilitating rigorous analytical treatment.

The developed methodology is applied to a range of problems arising in mathematical physics and continuum mechanics, including transonic flow, diffusion in heterogeneous media, and environmental processes. Throughout the text, theoretical developments are complemented by constructive solution methods and detailed analyses of mixed-type loaded equations.

Designed for researchers and specialists in partial differential equations, fractional calculus, mathematical physics, and applied mathematics, this book provides a comprehensive treatment of modern analytical approaches to nonlocal and mixed-type boundary value problems.

Zielgruppe

Academic

Autoren/Hrsg.

Agarwal, Praveen

Baltaeva, Umida

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Mathematik | Informatik Mathematik Mathematische Analysis Funktionentheorie, Komplexe Analysis
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle

Inhaltsverzeichnis

Chapter 1: Analogs of the Tricomi and Gellerstedt Problems. Chapter 2: Boundary value problems for loaded integro-differential equations with hyperbolic and parabolic–hyperbolic operators. Chapter 3: Boundary value problems for a class of third-order loaded differential equations. Chapter 4: Boundary value problems for loaded equations of mixed type with variable coefficients.

Über Autor(innen)

Praveen Agarwal has been recognized among the World’s Top 2% Scientists (2020–2025) as released by Stanford University. In the 2026 global ranking by Research.com, he was placed 13th in India and 1102th worldwide in Mathematics. With over 25 years of experience in teaching and research, Dr. Agarwal’s primary research interests include Special Functions, Fractional Calculus, Numerical Analysis, Differential and Difference Equations, Inequalities, and Fixed-Point Theory. He is a prolific researcher, having authored or edited 15 books and published more than 450 research papers in reputed national and international journals, in collaboration with nearly 100 mathematicians worldwide. According to Google Scholar, his work has received over 12,700 citations with an h-index of 59, while Scopus reports over 8,343 citations with an h-index of 49. He has served on the editorial boards of more than 50 journals and has edited 15 books. He has delivered invited talks and keynote lectures at numerous international conferences and institutions worldwide. In summary, P. Agarwal is a distinguished mathematician, educator, and academic leader whose contributions to research, teaching, and institutional development are widely recognized.

Umida Baltaeva is a Chief Researcher at the Khorezm Mamun Academy, Regional Branch of the Uzbekistan Academy of Sciences, Khiva, Uzbekistan. Her research interests include partial differential equations, mixed-type equations, loaded differential and integro-differential equations, fractional calculus, and mathematical physics. She has published numerous research articles in international peer-reviewed journals and has actively contributed to the development of the theory of loaded differential equations and mixed-type partial differential equations. Her recent research focuses on boundary value problems for loaded equations of classical and nonclassical types, mixed-type partial differential equations, fractional differential equations, and higher-order differential and integro-differential equations.