OPERATORS OF DIFFERENTIATION AND INTEGRATION OF FRACTIONAL ORDER AND THEIR APPLICATIONS

Abstract

newline I remember that what I now have was once amongst the things I only hoped for hence I extend my deep gratitude to my research supervisor Dr. Kisan Sharma Prof. and Head,Department of Mathematics for him assiduous guidance, support and impetus that had lead to the accomplishment of this work.I further extend my obligation and gratitude to Dr. Renu Jain, Professor, and Jiwaji University Gwalior (MP) for enabling me to carry out the work. I would like to sincerely acknowledge Dr. A. K. Sinha (Dean Research) and Dr. Ripu Ranjan Sinha (Associate dean research) Suresh Gyan Vihar University, Jaipur for the direction and commitment towards the university. Their visions in established focused research program and taking the standard to the highest level has helped me in transforming into a better researcher. I am thankful to Prof. (Dr.) A.S.Shekhawat, Department of mathematics Suresh Gyan Vihar University, Jaipur for providing me necessary facilities for carrying out the research work. For the motivation , enthusiasm, encouragement and immense knowledge in my livelihood and life, I offer my sincere thanks to Dr. R. D. Gupta, Dr. B. k. Singh, Dr. Omveer Singh and Dr. Y. M. Gupta. I am grateful to all my fellows at ITM Gwalior, especially Dr. Santosh K. Sharma, Dr. D. V.S. Kushwah, Dr. Manish Sharma, Dr. Smita Sharma, Dr. Neeta Saxena, Dr. M. S. Bhadauriya, Dr. D. S. Tomar, Mr. Akash Singhal, Ms. Ruchi Gangil, Dr. Arun Garg and all staff members of Department for their incessant co-operation and encouragement throughout the work. I owe a special thanks to Dr. Deerendra Mishra, Dr. Shimpi Singh Jadon, Dr. Amit Barnwal, Dr. Rishi Soni Dr. Rajendra S. Kushwah, Dr. Rajeev S. Rathore, Mr. D B V Singh ,Mr. Gaurav Dubey, and Mr. Vineet Shravastava. It is hard to overstate my solemn gratitude to my family for their massive love, support, encouragement, patience and prayers without which this attempt would have been worth nothing. I remain indebted of my wife who has pulled me through against impossible odds at times.