Differential equations play a vital role in the modeling of physical and engineering problems, such as those in solid and fluid mechanics, viscoelasticity, biology, physics, and many other areas. In general, the parameters, variables and initial conditions within a model are considered as being defined exactly. In reality there may be only vague, imprecise or incomplete information about the variables and parameters available. This can result from errors in measurement, observation, or experimental data; application of different operating conditions; or maintenance induced errors. To overcome uncertainties or lack of precision, one can use a fuzzy environment in parameters, variables and initial conditions in place of exact (fixed) ones, by turning general differential equations into Fuzzy Differential Equations ("FDEs"). In real applications it can be complicated to obtain exact solution of fuzzy differential equations due to complexities in fuzzy arithmetic, creating the need for use of reliable and efficient numerical techniques in the solution of fuzzy differential equations. These include fuzzy ordinary and partial, fuzzy linear and nonlinear, and fuzzy arbitrary order differential equations.
This unique work provides a new direction for the reader in the use of basic concepts of fuzzy differential equations, solutions and its applications. It can serve as an essential reference work for students, scholars, practitioners, researchers and academicians in engineering and science who need to model uncertain physical problems.
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Snehashish Chakraverty, Ph.D. is Professor of Mathematics at the National Institute of Technology, Rourkela in India, Ph. D. from IIT Roorkee and post-doctoral research from ISVR, University of Southampton, UK, and Concordia University, Canada. He was visiting professor at Concordia, McGill and Johannesburg universities. He published five books, 239 research papers, reviewer of many international journals, recipient of CSIR Young Scientist, BOYSCAST, UCOST, Golden Jubilee CBRI, INSA International Bilateral Exchange, Platinum Jubilee ISCA Lecture and Roorkee University gold medal awards. Dr. Chakraverty is the Chief Editor of International Journal of Fuzzy Computation and Modelling (IJFCM), Inderscience Publisher, Switzerland (http://www.inderscience.com/ijfcm) and happens to be the Guest Editor for other few journals. He was the President of the Section of Mathematical sciences (including Statistics) of Indian Science Congress (2015-2016) and was the Vice President – Orissa Mathematical Society (2011-2013). He has already guided eleven (11) Ph. D. students and seven are ongoing. Dr. Chakraverty has undertaken around 16 research projects as Principle Investigator funded by international and national agencies totaling about Rs.1.5 crores. His research area includes Differential Equations, Numerical Analysis, Soft Computing,Vibration and Inverse Vibration problems.
Smita Tapaswini, Ph.D. is Assistant Professor in the Department of Mathematics at the Kalinga Institute of Industrial Technology University in India and is also Post-Doctoral Fellow at the College of Mathematics and Statistics at Chongqing University in China. She has received her Ph.D. degree in Mathematics from National Institute of Technology Rourkela, Odisha, 769 008, India on January 2015. She has been awarded Rajiv Gandhi National Fellowship (RGNF), under University Grant Commission (UGC), Government of India and also qualified Graduate Aptitude Test in Engineering (GATE) in the year 2011. Her research interests include fuzzy differential equations, fuzzy fractional differential equations and numerical analysis.
Diptiranjan Behera, Ph.D. is working as a Post-Doctoral Fellow at the Sichuan Provincial Key Laboratory of Reliability Engineering, School of Mechatronics Engineering, University of Electronic Science and Technology of China (UESTC), China. After completing B. Sc. (Bachelor of Science) degree in 2008 with Mathematics honours from Banki College (Utkal University, Odisha, India), his career started from National Institute of Technology (NIT) Rourkela, Odisha 769008, India and did M. Sc. (Master of Science) and Ph. D. degree in Mathematics from there. He has completed his M. Sc. in the year 2010 and received his Ph. D. degree in January 2015. During Ph. D. he had been doing research as a Junior and Senior Research Fellow on a research project funded by Board of Research in Nuclear Sciences, Department of Atomic Energy, Government of India. His current research interest includes in the areas of interval and fuzzy mathematics, fuzzy finite element methods, fuzzy structural analysis, fuzzy differential equations, fuzzy fractional differential equations, fuzzy system of linear equations, fuzzy eigenvalue problem and fuzzy linear programming problem.
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