Fractional Differential Equations: Theory and Computations (2022)

Convener(s)


Name:	Dr. Navnit Jha	Prof. Harsha Hutridurga
Mailing Address:	Associate Professor, Department of Mathematics South Asian University, Akbar Bhawan, Chanakyapuri, New Delhi-110 021	Professor, Department of Mathematics Indian Institute of Technology Bombay, Powai, Mumbai, Maharashtra 400076
Email:	navnitjha at sau.ac.in	hutri at math.iitb.ac.in

The NCM Advanced Instructional School (AIS) on “Fractional Differential Equations:Theory and Computations” during December 12-24, 2022, through offline mode is going to organised at South Asian University (SAU), New Delhi. The broad topics to be covered in the Advanced Instructional School are Fractional calculus, Fractional ordinary differential equations (FODEs), Fractional partial differential equations (FPDEs), Approximation techniques for ODEs/PDEs with fractional order, Modeling fractional-order dynamical system, fractional diffusion, analytical and computational solutions of fractional differential equations. In addition to talks by the experts, interactive sessions with a significant amount of time being devoted to group discussions, and tutorials will be an integral part of the Advanced Instructional School. In this Advanced Instructional School, there will be regular lectures on all the topics provided by the speakers, and there will be a discussion on some among these that the participants have trouble getting across. The participants of NCM Advanced Instructional School include Ph.D. students, and young researchers.

Dates:

Monday, December 12, 2022 - 09:00 to Saturday, December 24, 2022 - 18:00

Venue:

South Asian University

Venue Address:

Department of Mathematics,
South Asian University, Akbar Bhawan,
Chanakyapuri, New Delhi-110 021

Venue State:

Delhi

Venue City:

New Delhi

PIN:

110021

Chrono Order:

419

Syllabus:

Syllabus:

Name of the Speaker with affiliation	No. of Lectures	Detailed Syllabus
Prof. Amiya K. Pani Professor, Department of Mathematics, Birla Institute of Technology and Science, Pilani-Goa Campus, Goa	6	Fractional ordinary differential equations and properties, Numerical solutions, Time-fractional diffusion equations, Fractional diffusion, Linear fractional equations and their properties, Theoretical studies, sub-diffusion, Current trends in fractional derivatives, Finite-difference method for fractional ODEs.
Professor K. Sreenadh Department of Mathematics, Indian Institute of Technology Delhi, Delhi	4	First order differential equation and its integral representation, Picard's method of successive approximations, Picard's theorem of local-in-time well-posedness, Maximal interval of existence and continuation, Lyapunov stability.
Prof. Samir Karaa Department of Mathematics and Statistics, Sultan Qaboos University Muscat, Oman	4	Fractional calculus, fractional integral, Riemann-Liouville fractional derivative, Caputo fractional derivative, Mittag- Leffler function, Fractional order evolution equation, Laplace transform.
Prof. Varsha S. Gejji Department of Mathematics, Savitribai Phule Pune University, Pune	6	Cauchy-type problems for ordinary differential equations of fractional order, Existence and uniqueness of solutions to Cauchy-type problems for ordinary differential equations of fractional order with Riemann-Liouville fractional derivative. Solvability of Cauchy-type problems with Caputo fractional derivative. Maximal interval of existence and the concept of continuation of solutions. Stability estimates for fractional order differential equations. Blow-up criteria in fractional order differential equations.
Prof. Harsha Hutridurga Department of Mathematics, Indian Institute of Technology Bombay, Mumbai	7	Elementary properties of Hilbert spaces, Orthogonality, Riesz representation theorem, Orthonormal basis, Mathematical modeling of diffusion and fractional diffusion equation, Long time asymptotic behavior of diffusion equation, Integral representation, Regularity and smoothing properties of diffusion equation.
Dr Yubin Yan Department of Mathematics, University of Chester, UK	6	Numerical method for fractional order ordinary differential equations, Backward Euler method, Second-order backward difference methods, Convolution, quadrature, Error estimate, Finite difference method for solving fractional diffusion equation, High-order approximation of Caputo fractional derivatives, Adaptive and high-order scheme for non-integer order differential equations.
Prof. Kapil K. Sharma Department of Mathematics South Asian University	1	Numerical method for ordinary differential equations
Dr. Navnit Jha Department of Mathematics South Asian University	2	Numerical method for heat equation.

References:

Bangti Jin, Fractional Differential Equations, An Approach via Fractional Derivatives, Springer
A.A. Kilbas, H.M. Srivastava, J.J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier

Time Table:

Time-Table (with names of speakers and course associates/ tutors):

Day	Date	Lecture 1 (9.30–11.00)	Tea (11.05 –11.25)	Lecture 2 (11.30–1.00)	Lunch (1.00–2.00)	Lecture 3 (2.00–3.30)	Tea (3.35-3.55)	Tutorial (4.00-5.00)	Snacks 5.05-5.30
		(name of the speaker		(name of the speaker)		(name of the speaker + tutors)		(name of the speaker + tutors)
Mon	12-12-22	L1 K. Sreenadh		L2 Samir Karaa		L3 K. Sreenadh		T1 KS, SKS, YS
Tues	13-12-22	L4 K. Sreenadh		L5 Varsha Shridhar Gejji		L6 Samir Karaa		T2 VSG, KS, YS
Wed	14-12-22	L7 Varsha Shridhar Gejji		L8 Samir Karaa		L9 Varsha Shridhar Gejji		T3 VSG, SK,NJ
Thu	15-12-22	L10 Varsha Shridhar Gejji		L11 Samir Karaa		L12 Yubin Yan		T4 VSG, NJ, PM
Fri	16-12-22	L13 Varsha Shridhar Gejji		L14 Varsha Shridhar Gejji		L15 Yubin Yan		T5 YY, PM, NK
Sat	17-12-22	L16 Kapil K. Sharma		L17 K. Sreenadh		L18 Yubin Yan		T6 YY, PM, NK
SUNDAY: OFF
Mon	19-12-22	L19 Harsha Hutridurga		L20 Harsha Hutridurga		L21 N. Jha		T7 HH,NJ, RKP
Tues	20-12-22	L22 Harsha Hutridurga		L23 Harsha Hutridurga		L24 N. Jha		T8 HH, NJ, RKP
Wed	21-12-22	L25 Amiya K. Pani		L26 Amiya K. Pani		L27 Harsha Hutridurga		T9 HH, NJ, RKP
Thu	22-12-22	L28 Harsha Hutridurga		L29 Amiya K. Pani		L30 Yubin Yan		T10 AKP, PD, TM
Fri	23-12-22	L31 Harsha Hutridurga		L32 Amiya K. Pani		L33 Yubin Yan		T11 AKP, PD, TM
Sat	24-12-22	L34 Amiya K. Pani		L35 Amiya K. Pani		L36 Yubin Yan		T12 AKP, PD, TM	Valedictory and feedback session

Tutorial Assistants:

S. No.	Name	Affiliation
1	Dr. Navnit Jha	Department of Mathematics, South Asian University, New Delhi
2	Dr. Saroj K. Sahani	Department of Mathematics, South Asian University, New Delhi
3	Dr. R. K. Pandey	Department of Mathematics, Indian Institute of Technology (BHU) Varanasi
4	Dr. P. Danumjaya	Department of Mathematics, BITS Pilani-K K Birla Goa Campus, Goa
5	Dr. T. Mathur	Department of Mathematics, BITS, Pilani, Rajasthan
6	Dr. Pankaj Mishra	Department of Mathematics, Deshbandhu College, University of Delhi, New Delhi
7	Dr. Neelesh Kumar	Department of Mathematics, Sri Venkateswara College, New Delhi.
8	Dr. Yashi	Shaheed Rajguru College of Applied Sciences, University of Delhi, Delhi

Full forms for the abbreviations of speakers and tutors:

HH: Harsha Hutridurga, KS: K. Sreenadh, VSG: Varsha Shridhar Gejji, AKP: Amiya K. Pani,

KKS: Kapil K. Sharma, SK: Samir Karaa,YY: Yubin Yan, PD: P. Danumjaya,NJ: Navnit Jha,

RKP: R. K. Pandey, SS: Saroj K. Sahani, TM: T. Mathur, PM: Pankaj Mishra,

NK: Neelesh Kumar, YS: Yashi

Selected Applicants:

Sr. n	SID no.	Full Name	Gender	Affiliation	Position in college/ university	Univ./ Ins M.Sc/ M.A	Year of passing M.Sc/ M.A
1.	44293	Kirti Rani	Female	Delhi Technological University	Research Scholar	Delhi Technological University	2021
2.	44308	Abhay Srivastava	Male	Delhi Technological University	Research Scholar	VBSPU Jaunpur	2017
3.	44331	Rashi Yadav	Female	University of Delhi	Research Scholar	G.J.U of Science and Technology, Hisar	2019
4.	44351	Mohd Rafiq	Male	University of Delhi	Research Scholar	University of Delhi	2016
5.	44432	Varela Pavankalyan	Male	National Institute of Technology, Kurukshetra	Research Scholar	National Institute of Technology, Rourkela	2020
6.	44434	Kuldeep Malik	Male	Dr. B. R. Ambedkar University, Delhi	Research Scholar	Kurukshetra University	2018
7.	44510	Debendra Prasad Panda	Male	BITS Pilani, K K Birla Goa Campus	Research Scholar	Berhampur University, Bhanja Bihar, Odisha	2018
8.	44533	Ritik Soni	Male	Central University of Punjab	Research Scholar	Indian Institute of Technology, Delhi	2019
9.	44537	Kirandeep Kaur	Female	Netaji Subhas University of Technology	Research Scholar	Indian Institute of Technology, Bhubaneswar	2018
10.	44548	Asha Kumari	Female	University of Delhi	Research Scholar	Central University of Jharkhand	2018
11.	44553	Hardagna Vatsal Vora	Male	Pandit Deendayal Energy University, Gandhinagar	Research Scholar	Kadi Sarva Vishwavidyalaya University	2018
12.	44609 NR	Bhawna Pokhriyal	Female	Dr. B.R. Ambedhkar University Delhi	Research Scholar	University of Delhi	2018
13	44628	Sangeeta Devi	Female	National Institute of Technology, Kurukshetra	Research Scholar	Kurukshetra University,Kurukshetra	2016
14	44651	Shridhar Kumar	Male	Indian Institute of Technology Patna	Research Scholar	Indian Institute of Technology Patna	2019
15	44711	Deepti Kaur	Female	Maitreyi College, University of Delhi	Assistant Professor	M.Sc. Mathematics from Hansraj College, University of Delhi	2009
16	44796	Amit Ujlayan	Male	Gautam Buddha University	Asst. Prof	CCSU Meerut	2001
17	44798	Raghvendra Kumar	Male	University of Hyderabad	Research Scholar	Indian Institute of Technology Guwahati	2019
18	44840	Swati	Female	Swami Shraddhanand College, University of Delhi	Assistant Professor	Dayalbagh Educational Institute,Agra	2009
19	44851	Rachana Shokhanda	Female	Dr. B.R. Ambedkar University Delhi	Research Scholar	Sri Vekateshwara College, University of Delhi	2013
20	44872	Ashish Yadav	Male	Birla Institute of Technology and Science, Pilani	Research Scholar	University of Delhi	2020
21	44909	Aasna Chauhan	Female	University of Delhi	Research Scholar	Rajasthan University	2018
22	44953	Kuldeep Kumar Tripathi	Male	Babasaheb Bhimrao Ambedkar University	Research Scholar	University of Lucknow	2016
23	44956	Arihant Patawari	Male	Indian Institute of Technology Patna	Research Scholar	BANARAS HINDU UNIVERSITY	2022
24	44975	Govind Singh	Male	Indian Institute of Technology Delhi	M.Sc. Student	IIT Delhi	2022
25	45061	Raghunath Bandha	Male	IIT Guwahati	Research Scholar	IIT Kharagpur	2020
26	45117	Paras Sharma	Male	University of Delhi	Research Scholar	South Asian University	2018
27	45120	Kartikay Khari	Male	Delhi Technological University	Research Scholar	South Asian University	2015
28	45194	Shweta Kumari	Female	IIT Delhi	Research Scholar	IIT ISM Dhanbad	2019
29	45213	Lalit Kumar	Male	Govt. PG college Faridabad	Research Scholar	IIT Bombay	2015
30	45219	Yash Vats	Male	IIT Delhi	Research Scholar	IIT Delhi	2022

Wait listed Candidate:

1	45232	Mohammad Saif	Male	Jamia Millia Islamia, New Delhi	Research Scholar	Jamia Millia Islamia, New Delhi	2020
2	44521	Ashish Kumar	Male	Dr Br Ambedkar University Delhi	Research Scholar	University of Delhi	2019

How to Reach:

TBA

School Short Name:

fdetc

Last Date Application:

Friday, April 15, 2022

School Type:

AIS