Understanding Integro-Differential Equations

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J. Vasundhara Devi, PhD – Professor in Mathematics, GVP – Prof. V. Lakshmikantham Institute for Advanced Studies, GVP College of Engineering, Andhra Pradesh, India
Zahia Drici, PhD – Professor and Chair, Department of Mathematics, Illinois Wesleya University, Bloomington, IL, USA
Farzana A. McRae, PhD – Department of Mathematics, Catholic University of America, Washington D.C., USA

Series: Mathematics Research Developments
BISAC: MAT007000
DOI: https://doi.org/10.52305/NRLJ6556

This book presents an overview of the theory of Integro-Differential Equations (InDEs). Beginning with the history of the inception of InDEs, the existence and uniqueness results for the initial value problem of InDEs is given. Next, stability concepts are discussed, including Lyapunov stability and Ulam-Rassias stability. Numerical techniques and operational matrix methods are also introduced. A specific study of second order InDEs of Fredholm InDes in complex plane is presented and an application to Finance is given.

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Table of Contents

Preface

Chapter 1. An Overview of Existence Results for Some Integro-Differential Equations
CH. V. Sreedhar, I. S. N. R. G. Bharat and J. Vasundhara Devi
Department of Mathematics, GVP-Prof. V. Lakshmikantham Institute for Advanced Studies, Gayatri Vidya Parishad College of Engineering (Autonomous), Visakhapatnam, AP, India

Chapter 2. A Brief Overview of the Stability Theory of Integro-Differential Equations
Z. Drici1, F. A. McRae2 and J. Vasundhara Devi3
1Department of Mathematics, Illinois Wesleyan University, Bloomington, Illinois, USA
2Department of Mathematics, Catholic University of America, Washington DC, USA
3Department of Mathematics and GVP Profssor, V. Lakshmikantham Institute for Advanced Studies, Gayatri Vidya Parishad College of Engineering, Visakhapatnam, AP India

Chapter 3. Advances in the Qualitative Theory of Integro–Differential Equations
Osman Tunç1, Seenith Sivasundaram2 and Cemil Tunç3
1Department of Computer Programing, Baskale Vocational School, Van Yuzuncu Yil University, Van, Turkey
2Department of Mathematics, College of Science Engineering and Mathematics, Daytona Beach, Florida, USA
3Department of Mathematics, Faculty of Sciences, Van Yuzuncu Yil University, Campus, Van, Turkey

Chapter 4. Mathematical Methods for Integro-Differential Equations and Their Applications
Gunvant A. Birajdar1, N. Giribabu2
1School of Rural Development, Tata Institute of Social Sciences Tuljapur, Osmanabad, India
2Department of Mathematics, Gayatri Vidya Parishad College of Engineering, Visakhapatnam, India

Chapter 5. Operational Matrices for Solving Fractional Order Integral and Integro-Differential Equations
H. Tajadodi1, R. M. Ganji2, S. M. Narsale3 H. Jafari4
1Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran
2Department of Applied Mathematics, University of Mazandaran, Babolsar, Iran
3Symbiosis Institute of Technology, Symbiosis International (Deemed University), Pune, India
4Department of Mathematical Sciences, University of South Africa, South Africa

Chapter 6. On a Second Order Nonlinear Integro-Differential Equation of Fredholm Type in a Complex Plane
LEMITA Samir, SELIM Raja and BELAHBIB Zeineb

Chapter 7. Linear and Nonlinear Partial Integro-Differential Equations Arising from Finance
Jos´e Cruz1, Maria Grossinho1, Daniel Sevcovic2 and Cyril Udeani2
1ISEG, University of Lisbon, Portugal
2Comenius University in Bratislava, Slovakia

Index

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