# Registered Data

Contents

- 1 [CT052]
- 1.1 [01893] Existence and blow-up solutions of fractional reaction-diffusion system of SPDEs
- 1.2 [02222] Unfolding operator in Heisenberg group and its applications
- 1.3 [02027] Understanding Difference Equation System Models using Telescoping Sums Method
- 1.4 [02453] Allee effects, Evolutionary game, and Ideal free strategies in Partial Migration Population
- 1.5 [00005] ON E-STATISTICAL SUMMABILITY OF BOUNDED SEQUENCE

# [CT052]

## [01893] Existence and blow-up solutions of fractional reaction-diffusion system of SPDEs

**Session Date & Time**: 5D (Aug.25, 15:30-17:10)**Type**: Contributed Talk**Abstract**: In this talk, we investigate the existence and finite-time blowup solution of a reaction-diffusion system of stochastic partial differential equations (SPDEs) driven by two dimensional fractional Brownian motion. We provide sufficient conditions for the existence of a global solution. Moreover, we provide lower and upper bounds for the finite-time blowup solution of the system of SPDEs and obtain the lower and upper bounds for the probability of non-explosive solutions to our considered system**Classification**:__35R60__,__60H15__,__74H35__**Author(s)**:**Sankar Subramani**(Periyar University, Salem, Tamilnadu.)- Manil T Mohan (Indian Institute Of Technology, Roorkee)
- Karthikeyan Shanmugasundaram (Periyar University, Salem, Tamilnadu.)

## [02222] Unfolding operator in Heisenberg group and its applications

**Session Date & Time**: 5D (Aug.25, 15:30-17:10)**Type**: Contributed Talk**Abstract**: After the development of multi-scale convergence in the 1990s, the periodic unfolding approach is one of the most effective methods for studying multi-scale problems like homogenization in the Euclidean setup. This talk will discuss the periodic unfolding operator in the Heisenberg group. Analogous to the Euclidean unfolding operator, we prove all the required properties. We apply the unfolding operator to homogenize an optimal control problem subject to a state equation having high contrast diffusive coefficients.**Classification**:__35Rxx__**Author(s)**:**Abu Sufian**(TIFR- Centre for Applicable Mathematics)- Akambadath Keerthiyil Nandakumaran (Indian Institute of Science, Bangalore, India)

## [02027] Understanding Difference Equation System Models using Telescoping Sums Method

**Session Date & Time**: 5D (Aug.25, 15:30-17:10)**Type**: Contributed Talk**Abstract**: Difference equations frequently appear as discrete mathematical models of various biological and environmental phenomena. In this paper, the authors study the following systems: \begin{equation*} x_{n+1} = \dfrac{x_{n-3}}{\pm 1 \pm y_n x_{n-1} y_{n-2} x_{n-3}},\ \ y_{n+1} = \dfrac{y_{n-3}}{\pm 1 \pm x_n y_{n-1} x_{n-2} y_{n-3}}, \end{equation*} which were first considered by Elsayed in 2015, and results were proven using mathematical induction. This time, the authors present the solution forms of each system using telescoping sums technique. The advantages and disadvantages of the two methods are discussed. Boundedness and convergence of solutions shall be presented.**Classification**:__39A05__,__39A22__,__65Q10__**Author(s)**:**Jerico Bravo Bacani**(University of the Philippines Baguio)- Julius Fergy Tiongson Rabago (Kanazawa University)

## [02453] Allee effects, Evolutionary game, and Ideal free strategies in Partial Migration Population

**Session Date & Time**: 5D (Aug.25, 15:30-17:10)**Type**: Contributed Talk**Abstract**: Allee effect is a density-dependent phenomenon in which population growth or individual components of fitness increase as population density increases. Understanding the density-dependent effect is vital to elucidate how populations evolve and to investigate evolutionary stability. Partial migration, where a proportion of a population migrates while other individuals remain resident, is widespread across most migratory lineages. However, the mechanism is still poorly understood in most taxa, especially those experiencing positive density-dependent effects. In this talk we discuss the evolutionary stability of partial migration population with the only migrant population experiencing Allee effects. Using the Evolutionary Game Theoretic (EGT) approach, we show the existence and uniqueness of a evolutionary stable strategy (ESS). We also show that the ESS is the only Ideal Free distribution (IFD) that arises in the context of a partially migrating population.**Classification**:__39A60__,__92D25__,__91A22__**Author(s)**:- Yogesh Trivedi (Bits-Pilani, K.K Birla Goa Campus)
- Ram Singh (Bits-Pilani, K.K Birla Goa Campus)
**Anushaya Mohapatra**(Bits-Pilani, K.K Birla Goa Campus)

## [00005] ON E-STATISTICAL SUMMABILITY OF BOUNDED SEQUENCE

**Session Date & Time**: 5D (Aug.25, 15:30-17:10)**Type**: Contributed Talk**Abstract**: A summability method is said to be regular if it preserves the limit, i.e., it sums all convergent series to its Cauchy's sum. In this paper, we have introduced the sequence space X(E) defined by the Euler matrix for the spaces X = l_∞, c, c_0 and l_p, (1 ≤ p < ∞). Some fundamental properties and relations related to these spaces are examined. A new regular statistical summability method (Euler statistical summability) is given. The graph for Euler and Euler statistical summability is given by using MATLAB(2018a).**Classification**:__40B05__,__40CXX__,__54A20__**Author(s)**:**SABIHA TABASSUM**(ALIGARH MUSLIM UNIVERSITY ALIGARH)