An International training workshop on “Computational Special Functions and Their Applications” was organized by MathTech Thinking Foundation, INDIA in collaboration with Department of Mathematics and Humanities, Sardar Vallabhbhai National Institute of Technology, Gujarat, INDIA; Department of Mathematics, Punjabi University, Patiala, INDIA; Department of Mathematics, Baba Farid College, Bathinda, INDIA; Department of Mathematics, Sardar Patel University, Anand, INDIA; School of Science and Humanities, Poornima University, Jaipur, INDIA; Department of Mathematics, Ecole Normale Superieure de Meknes, Moulay Ismail University, MOROCCO from April 5 to 7, 2022. 846 delegates from Ethiopia, India, Ghana, Kenya, Nigeria and Malaysia from different backgrounds and professions like research scholars, National and International faculty members from Universities/ Institutes, Engineers, people from academia, and Post Graduate Students participated in this International Training Workshop.

The main objective of the training workshop is to provide a comprehensive overview of special functions and their applications in other branches of Science with emphasis on computing special functions with MATLAB. The workshop will provide an excellent opportunity for participants to meet and exchange ideas of common interests and to discuss new challenges faced by our academic community working in this area from different institutions and universities around the world. The training will motivate and educate the participants to undertake research in this field. The expected outcome from this event is for the participants to be able to confidently carry out research in this field and also apply it to real-world problems. The procedure we intend to use in achieving this is by having resource persons who are knowledgeable in this field to deliver their talk and guide the participants on how to apply the special functions to real-life problems. Our desire is to leave an impact on the students and researchers to help them with research in the field of computing special functions and their applications.  A feedback form will be circulated to the participant and their suggestion will add to effective decision-making about future conferences and also to monitor the participation of delegates. Since everyone is from different geographical locations and restrictions on movement are a barrier to training like this, the training will be done virtually to enable participants from different parts of the world.

The targeted audience includes research scholars, National and International faculty members from Universities/ Institutes, Engineers, people from academia, and Post Graduate Students

The entire International Training Workshop wrapped up after three days of wonderful scientific interaction, many knowledgeable experiences and a promise of yet another interaction in future. DAY 1

The ‘International Training Workshop on Computing Special Functions and Their Applications’ was inaugurated on April 05, 2022 with the opening address by Prof. Abdulvahid H. Hasmani followed by the welcome address by Dr. Satya Bir Singh, Professor, Department of Mathematics, Punjabi University, Patiala. Prof. Ajay Kumar Shukla threw light on various aspects of the workshop. He emphasized that the primary aim of the training workshop includes a comprehensive overview of special functions and their applications in other branches of Science. The main theme of the training workshop revolves around computing special functions using various tools of MATLAB by focusing on motivating and educating the participants on essentials to make research in this field. The procedure intended to be used in achieving this is by having resource people that are knowledgeable in this field to deliver their talk and guide the participants on how to apply the special functions to real life problems.

The first technical session of the first day focused on ‘Mittag-Lefller function and its applications for real-world problems’. The resource person in first technical session was Prof. Dumitru Baleanu, Institute of Space Sciences, Romania. He is well known Physicist and highly cited researcher in Mathematics since 2015. The talk was very useful particularly the deliberations on real life applications.

The second talk was delivered by Prof. Ajay Kumar Shukla, Department of Mathematics and Humanities, Sardar Vallabhbhai National Institute of Technology, Surat. The learned speaker presented his views on the topic ‘Some facts on pRq function’. Beginning with Generalized Mittag Leffer Functions, he briefly explained Fourier and Euler-type Integral Representation of the R-function along with some applications of R-function.

In the third session Dr. Prashan Patel, Department of Mathematics, Sardar Patel University, Vallabh Vidyanagar presented his views on the topic ‘Study of Some Special Functions using MATLAB’. Beginning with Script File, he discussed the process of plotting complex domain functions with the help of an example. The session was very useful and thought provoking.

DAY 2

The second day of the ‘International Training Workshop on Computing Special Functions and Their Applications’ started with the first technical session by Dr. Jyotindra C. Prajapati, Department of Mathematics, Sardar Patel University, Vallabh Vidyanagar on the topic ‘Solution of Laplace Transforms in terms of Error functions’. The learned speaker started his lecture with a brief introduction of generalized gamma function and its role in complimentary error function. He discussed Laplace and inverse Laplace transforms of some complicated functions using convolution theorem.

Next invited talk wasgiven by Dr. Mehar Chand, Department of Mathematics, Baba Farid College, Bathinda. He shared his views on the topic ‘Numerical and Graphical interpretation of (p,q)-Mittag-Leffler Functions using MATLAB’. The resource person started his talk by bringing out the importance of numerical and graphical interpretation of functions for their application in engineering. He discussed some numerical results regarding k-Mittag-Leffler Functions using simple MATLAB programs. 

In the third technical session, we had Dr. Ranjan Kumar Jana, Department of Mathematics and Humanities, Sardar Vallabhbhai National Institute of Technology, Surat as resource person. His topic of discussion was ‘Bessel Function and connection with Ramanujan’s Mathematics’. The learned speaker deliberated in detail on the background and generalizations of Bessel Functions along with various integrals involving Bessel Functions and generalized Bessel matrix functions. Dr. Jana discussed  ‘Computation of Bessel and Error Function through Mathematica’. He emphasized in detail about the fields ranging from standard arithmetic to calculus, algebra and numerical analysis where Mathematica can come to the forefront for helping researchers to obtain fruitful results.

DAY 3

The third day of the ‘International Training Workshop on Computing Special Functions and Their Applications’ started with the first technical session by Dr. Sunil Dutt Purohit on the topic ‘On family of incomplete I-functions and their applications’. The learned speaker started his lecture with a brief introduction of incomplete I-functions and their basic properties. He also discussed various applications of incomplete I-functions with a particular reference to internal blood pressure problem.

The second technical session was by Dr. Shilpi Jain, Department of Mathematics, Poornima College of Engineering, Jaipur whose topic of discussion was ‘Study of Fractional Hypergeometric Functions and their Applications’. In the beginning, Dr. Jain briefly explained classical beta and gamma functions. She then discussed extended hypergeometric functions and also explained that fractional calculus operators having various special functions can be used for modelling of system in turbulence and fluid dynamics.

In the third technical session, we had Dr. Mohammad Sajid, Department of Mechanical Engineering, Qassim University, Saudi Arabia as resource person. His topic of discussion was ‘Fractals and Chaos in Some Kinds of Special Functions with Demonstration by MATLAB’.  The learned speaker emphasized that MATLAB programming loops are a crucial way to generating fractals. He emphasized that MATLAB tools can be extensively applied in the study of chaos and fractals.

This was a wonderful virtual workshop, which made us realize that we need to practice MATLAB in real mode. The sessions ended by presenting a certification to the expert speakers. All the session were very interesting and appreciated by the attendees. Overall, the workshop has wrapped up on a promising note. It was a useful interaction that is sure to motivate many aspirants. Sharing our experiences with some of leading researchers was a golden opportunity for us and we are thankful for that. We look forward to such interactions in the near future. We are grateful to all experts, for their wisdom and above all, we appreciated their willingness to spend their valuable time with us. In all, it was an absolute honor to share space with you all even though virtual space.

Hon Vice Chancellor Punjabi University Patiala was kind enough to accept the invitation to be the chief guest of Valedictory function and to deliver valedictory address. At the end, Dr. Satyabir Singh shared the overall report of the event with us and she also acknowledged the appreciation from the participants. Dr. Ranjan Kumar Jana presented a brief remarks of the training workshop and also expressed her gratitude to the entire team working around the clock to make this event successful. After that Dr. Sudhi Rajive proposed a vote of thanks.  She expressed her deep sense of appreciation to all the members for their valuable support and presented his gratitude to the participants for their invaluable support. She acknowledged the Convener, Organizing Committee members, secretaries, organizing chairperson and Students Volunteers. They shared their experience and reviews during this workshop. She also thanked the entire participant for their active participation and patience during the workshop. She thanked all the members who worked tirelessly for the success of the event. The workshop ended with national anthem.

Convenor(s)

Prof. Ajay Kumar Shukla: Department of Mathematics and Humanities, SVNIT, Surat, Gujarat, INDIA

Prof. Satya Bir Singh: Department of Mathematics, Punjabi University, Patiala, INDIA

Prof. Mohammed Amine: Director, Ecole Normale Supérieure, Moulay Ismail University, Marjane 2, Meknes, MOROCCO

Dr. Abdulvahid H. Hasmani: Professor & Head, Department of Mathematics, Sardar Patel University, Vallabh Vidyanagar, Anand, Gujarat, INDIA

Prof. Sudhi Rajiv: Dean, International Relations & Professor of English and Soft Skills, Poornima University, Jaipur, INDIA

Dr. Manish Bansal: Vice-Principal, Baba Farid College, Bathinda, INDIA

Dr. Gurmej Singh Sandhu: General Secretary, MathTech Thinking Foundation, INDIA

Resource Person(s)

Prof. Dumitru Baleanu: Institute of Space Sciences, Bucharest, ROMANIA

Prof. Ajay Kumar Shukla: Department of Mathematics and Humanities, SVNIT, Surat, Gujarat, INDIA

Dr. Sunil Dutt Purohit: Department of HEAS (Mathematics), Rajasthan Technical University, Kota, INDIA

Dr. Shilpi Jain: Associate Professor, Department of Mathematics, Poornima College of Engineering, Jaipur, INDIA

Dr. Mohammad Sajid: Department of Mechanical Engineering, College of Engineering, Qassim University, SAUDI ARABIA

Dr. Ranjan Kumar Jana: Department of Mathematics and Humanities, SVNIT, Surat, Gujarat, INDIA

Dr. Prashantkumar Patel: Department of Mathematics, Sardar Patel University, Vallabh Vidyanagar, Anand, Gujrat, INDIA

Organizing Secretaries

Dr. Jyotindra C Prajapati: Department of Mathematics, Sardar Patel University, Vallabh Vidyanagar, Anand, Gujarat, INDIA

Dr. Ranjan Kumar Jana: Department of Mathematics and Humanities, SVNIT, Surat, Gujarat, INDIA

General Chair

Dr. Mehar Chand: Department of Mathematics, Baba Farid College, Bathinda, India & President, MathTech Thinking Foundation, INDIA

Organizing Committee

Prof. Zakia Hammouch: Head, Department of Sciences, ENS, Moulay Ismail University, Marjane 2, Meknes, MOROCCO

Prof. Satya Bir Singh: Department of mathematics, Punjabi University, Patiala, INDIA

Dr. Randhir Singh Baghel: Associate Professor of Mathematics, School of Science & Humanities, Poornima University, Jaipur, INDIA

Dr. Gurmej Singh Sandhu: Department of Mathematics, Mata Sahib Kaur Girls College, Talwandi Sabo, Bathinda, INDIA

Mr. Navneet Garg: Department of Mathematics, Baba Farid College, Bathinda, INDIA

Dr. Sarita Rani: Department of Mathematics, Baba Farid College, Bathinda, INDIA

Dr. N. S. Noorie: Professor, Department of Mathematics, Punjabi University, Patiala, INDIA

Dr. Shrikant: Assistant Professor of Physics, School of Science & Humanities, Poornima University, Jaipur, INDIA

Dr. Narinder Singh: Ph.D.(Department of mathematics), Punjabi University, Patiala, INDIA

Scientific Committee

Dr. Zarife Zararsiz: Department of Mathematics, Nevşehir Hacı Bektaş Veli, TURKEY

Dr. Ebenezer Bonyah: Department of Mathematics, Akenten Appiah Menka University of Skills Training and Entrepreneurial and Entrepreneurial, AAMUSTED Ghana

Dr. Hanaa Hachimi: BOSS team, GS laboratory, ENSA of Kenitra Ibn Tofail University, University campus PO Box 242, Kenira14000, Morocco

Dr. Bharti V. Nathwani: Department of Mathematics, Amity School of Applied Sciences, Amity University, Mumbai, INDIA

Dr. O. Ravi: Professor, PMT College Usilamputti, Madurai (TN), INDIA

Dr. S. K. Jain: Professor, Department of Civil Engineering, MITS Gwalior, INDIA

Dr. Amit Parmar: Assistant Professor of Mathematics, School of Science & Humanities, Poornima University, Jaipur, INDIA

Dr. K. P. Ghadle: Prof and Head, Department of Mathematics, BAMU, Aurangabad, INDIA

Dr. Harbhajan Singh: Department of Mathematics, Baba Farid College, Bathinda, INDIA

Dr. Özen ÖZER: Department of Mathematics, Kırklareli Üniversitesi, TURKEY

Dr. Payal Singla: Department of Mathematics, Guru Nanak College Killianwali, District Sri Muktsar Sahib, INDIA.

Student Volunteer(s)

Mrs. Meetu Jain (Research Scholar), Department of Mathematics, Punjabi University, Patiala, Punjab, INDIA

Mr. Pushwinder Kumar (Research Scholar), Department of Mathematics, Punjabi University, Patiala, Punjab, INDIA

Jiya Kukkar: MTTF Intern, Department of Mathematics, Baba Farid College, Bathinda, INDIA

Alka Rani: MTTF Intern, Department of Computer Science, Baba Farid College, Bathinda, INDIA

Jatin  Manchanda: MTTF Intern, Department of Physics, Baba Farid College, Bathinda, INDIA

Baljinder Singh: MTTF Intern, Department of Computer Science, Baba Farid College, Bathinda, INDIA

Shaina Rani: MTTF Intern, Department of Mathematics, Baba Farid College, Bathinda, INDIA

Mehak Dhir: MTTF Intern, Department of Computer Science, Baba Farid College, Bathinda, INDIA

Jatin Goyal: MTTF Intern, Department of Computer Science, Shahid Bhagat Singh Govt College, Kotkapura, INDIA

Gurwinder Singh: MTTF Intern, Department of Computer Science, Baba Farid College, Bathinda, INDIA

Harshal Gharat: Department of Mathematics, Amity School of Applied Sciences, Amity University, Mumbai, INDIA

Cynthia Dias: Department of Mathematics, Amity School of Applied Sciences, Amity University, Mumbai, INDIA

Shital Patil: Department of Mathematics, Amity School of Applied Sciences, Amity University, Mumbai, INDIA