# Registered Data

Contents

- 1 [CT012]
- 1.1 [00335] Fractional Relaxation-Oscillation and Fractional Biological Population Equations: Applications of the Elzaki Decomposition Method
- 1.2 [00422] On Some fractional integrodifferential equations using $\psi$ Hilfer fractional operator
- 1.3 [00661] A variational methods for fractional Sturm-Liouville eigenvalue problem
- 1.4 [00853] Numerical Approximation of Fractional Burgers Equation with Non-singular Time-Derivatives
- 1.5 [00928] Controllability of Fractional Evolution Systems with Impulses.
- 1.6 [01090] A high order approximation scheme for non-linear time fractional reaction-diffusion equation
- 1.7 [01981] An Efficient Computational Technique for Semilinear Time-Fractional Diffusion Equation
- 1.8 [01992] A new approach to solve a class of fractional order variational problem
- 1.9 [02168] Controllability Result of Fractional Semi-Linear System with Diffusion on a boundary subregion.
- 1.10 [02390] Discontinuous Galerkin method for time-fractional delay differential equation
- 1.11 [02467] Existence of unique blow-up solutions to fully fractional thermostat models
- 1.12 [02540] Dynamics of Fractional Order Crime Transmission Model with Fear Effect and Gang-war
- 1.13 [02607] Composition of Saigo’s k-Fractional Integral and Derivative Operators
- 1.14 [02621] Effect of magnetic field on natural convection through infinite plates with ramped velocity
- 1.15 [01966] Fekete-Szegö Inequality for Universally Prestarlike Functions By a Variational Method

# [CT012]

## [00335] Fractional Relaxation-Oscillation and Fractional Biological Population Equations: Applications of the Elzaki Decomposition Method

**Session Date & Time**: 3C (Aug.23, 13:20-15:00)**Type**: Contributed Talk**Abstract**: In various suitable habitat scenarios, the Elzaki decomposition method is used to handle the fractional order relaxation and damped oscillation equation along with the time-fractional spatial diffusion biological population model. According to the graphs for the found solutions, fractional relaxation is a super-slow phenomenon due to its protracted descent, and fractional damped oscillation is an intermediate process that explains damped oscillation dynamic systems generated by some attenuated oscillations. The biological population model of time-fractional spatial diffusion portrays a rapid increase in population density in an ecosystem migrating from an unfavourable zone to a good habitat.**Classification**:__26A33__,__33E12__,__35A22__,__34C26__,__60J70__**Author(s)**:**Daya Lal Suthar**(Wollo University)

## [00422] On Some fractional integrodifferential equations using $\psi$ Hilfer fractional operator

**Session Date & Time**: 3C (Aug.23, 13:20-15:00)**Type**: Contributed Talk**Abstract**: In this talk we present the study some properties of fractional integrodifferential equations. We have studied the equations using $\psi$ fractional derivative and $\psi$ Riemann-Liouville integral operator. The existence and uniqueness solution is studied. Schaefer's fixed point theorem and Banach contraction principle is used for obtaining the results.**Classification**:__26A33__,__34A08__,__34A12__,__34A40__**Author(s)**:**Deepak B Pachpatte**(Dr. Babasaheb Ambedkar Marathwada University)

## [00661] A variational methods for fractional Sturm-Liouville eigenvalue problem

**Session Date & Time**: 3C (Aug.23, 13:20-15:00)**Type**: Contributed Talk**Abstract**: we consider a regular Fractional Sturm--Liouville Problem (FSLP) of order $ \mu $ ($ 0 <\mu <1 $). We approximate the eigenvalues and eigenfunctions of the problem using fractional variational methods. Here, we extend the theories for fractional order $1/2 < \mu <1$ to $ 0 <\mu <1 $. Using variational methods, we approximate FSLP and obtain the eigenvalues and eigenfunctions of the problem. We also prove that the FSLP has a countably infinite increasing sequence of eigenvalues and corresponding eigenfunctions.**Classification**:__26A33__,__34A08__,__34B24__,__35R11__**Author(s)**:**Prashant Kumar Pandey**(Vellore Institute of Technology (VIT) Bhopal University)- Rajesh K. Pandey (Department of Mathematical Sciences, Indian Institute of Technology (BHU) Varanasi, Varanasi)
- Om P Agrawal (Mechanical Engineering and Energy Processes, Southern Illinois University, Carbondale, IL)

## [00853] Numerical Approximation of Fractional Burgers Equation with Non-singular Time-Derivatives

**Session Date & Time**: 3C (Aug.23, 13:20-15:00)**Type**: Contributed Talk**Abstract**: Fractional Burgers equation (FBE) is a partial differential equation being non-linear in space. This work presents a numerical method to solve a time-FBE with second order of convergence. The fractional time-derivative is taken as non-singular derivative whose kernel contains the Mittag-Leffler function. The discretization of derivatives is done by using finite difference method and Newton iteration method. Developed numerical scheme is stable and convergent in L^∞ norm. Examples have been illustrated to validate the theory.**Classification**:__26A33__,__65R10__,__35R11__**Author(s)**:**Swati Yadav**(NTNU Trondheim)- Swati Yadav (NTNU Trondheim)
- Rajesh Kumar Pandey (IIT BHU, Varanasi)

## [00928] Controllability of Fractional Evolution Systems with Impulses.

**Session Date & Time**: 3C (Aug.23, 13:20-15:00)**Type**: Industrial Contributed Talk**Abstract**: In this article, we establishes a set of sufficient conditions for the controllability of fractional semilinear evolution inclusions with state dependent delay and interval impulses involving the caputo derivative in Banach spaces. For our results, we used fixed point theorem for condensing maps due to Bohnenblust-Karlin and α- resolvent family . As an application, the controllability of a fractional partial differential equations is discussed and verified our main results.**Classification**:__26A33__,__34A37__,__93B05__,__34A34__,__34A08__**Author(s)**:**Malar Kandasamy**(Bharathiar University )- Sandeep Ganesan (Anna University)

## [01090] A high order approximation scheme for non-linear time fractional reaction-diffusion equation

**Session Date & Time**: 3D (Aug.23, 15:30-17:10)**Type**: Contributed Talk**Abstract**: We discuss a high order numerical scheme for the non-linear time fractional reaction-diffusion equation of order $\alpha\in (0, 1)$. A cubic approximation and compact finite difference schemes are used to approximate the time-fractional and spatial derivatives respectively. The numerical scheme achieves convergence rate of order $4-\alpha$ in the temporal direction and $4$ in the spatial direction. Further, numerical experimentation is performed to demonstrate the authenticity of the proposed numerical scheme.**Classification**:__26A33__,__35R11__,__35A35__**Author(s)**:**Rajesh Kumar Pandey**(Indian Institute of Technology (BHU) Varanasi)- Deeksha Singh (Indian Institute of Technology (BHU) Varanasi)

## [01981] An Efficient Computational Technique for Semilinear Time-Fractional Diffusion Equation

**Session Date & Time**: 3D (Aug.23, 15:30-17:10)**Type**: Contributed Talk**Abstract**: We will discuss a semilinear time-fractional diffusion equation where the time-fractional term includes the combination of tempered fractional derivative and $k$-Caputo fractional derivative with a parameter $k \geq 1$. The semi-analytical solution is obtained using the Elzaki decomposition method. The quasilinearized problem is discretized by tempered $_kL2$-$1_\sigma$ method. Stability and convergence analysis have been discussed using the energy method. In support of the theoretical results, a numerical example has been incorporated.**Classification**:__26A33__,__35A22__,__35R11__,__65M06__,__65M15__,__Computational Methods for Fractional Differential Equation__**Author(s)**:**Aniruddha Seal**(Indian Institute of Technology Guwahati)- Natesan Srinivasan (Indian Institute of Technology Guwahati)

## [01992] A new approach to solve a class of fractional order variational problem

**Session Date & Time**: 3D (Aug.23, 15:30-17:10)**Type**: Contributed Talk**Abstract**: In this work, a numerical approach is presented to solve a class of fractional variational problems (FVPs). We obtained operational matrices based on the Hosoya polynomial for fractional order integration and multiplication together with the Lagrange multiplier method for the constrained extremum. An error estimate of the numerical solution is proved for the approximate solution obtained by the proposed method.**Classification**:__26A33__,__35A15__**Author(s)**:**Hossein Jafari**(University of South Africa)

## [02168] Controllability Result of Fractional Semi-Linear System with Diffusion on a boundary subregion.

**Session Date & Time**: 3D (Aug.23, 15:30-17:10)**Type**: Contributed Talk**Abstract**: The main objective of this work is to investigate the regional boundary controllability problems for a class of semi-linear fractional sub-diffusion equations. In particular, sufficient conditions are derived for the regional boundary controllability by assuming that the associated linear system is approximately regionally boundary controllable. Further, the main result is obtained by using the fractional powers of operators and fixed point technique where we suppose that the associated linear system is approximately controllable on a suitable sub-region of the system’s evolution domain. In addition, we present some numerical simulations worked out in the end to illustrate the effectiveness of our theoretical result.**Classification**:__26A33__**Author(s)**:**Asmae TAJANI**(Moulay Ismail University)

## [02390] Discontinuous Galerkin method for time-fractional delay differential equation

**Session Date & Time**: 3D (Aug.23, 15:30-17:10)**Type**: Contributed Talk**Abstract**: In this article, we analyze the discontinuous Galerkin method for time-fractional partial differential equation with delay term $u(\theta(t))$, where $\theta(t)=t-\tau(t)< t$. The well-posedness of the fully discrete scheme for a fractional delay system is investigated. Also, we show the optimal order of convergence in the energy norm. Some numerical results are provided to support theoretical results.**Classification**:__26A33__,__35D30__,__65M60__,__34K37__**Author(s)**:**Raksha Devi**(Department of Mathematics, Indian Institute of Technology, Roorkee )- Dwijendra N. Pandey (Department of Mathematics, Indian Institute of Technology, Roorkee )

## [02467] Existence of unique blow-up solutions to fully fractional thermostat models

**Session Date & Time**: 3E (Aug.23, 17:40-19:20)**Type**: Contributed Talk**Abstract**: A thermostat is a device that detects the temperature of a physical system and takes the requisite actions to maintain the system's temperature at a predetermined set point. This paper deals with a fully fractional thermostat model involving Riemann-Liouville fractional derivatives. By choosing an appropriate weighted Banach space of continuous functions, we employ the Banach contraction principle to establish the existence and uniqueness result. An example is presented to validate our theoretical finding.**Classification**:__26A33__,__34A08__,__34K10__,__34K37__,__65L10__,__Fractional differential equations, Riemann-Liouville fractional derivative, Thermostat model, Banach contraction principle, Product rectangle rule, Numerical simulation.__**Author(s)**:**KIRAN KUMAR SAHA**(Indian Institute of Technology Roorkee)- NAGARAJAN SUKAVANAM (Indian Institute of Technology Roorkee)

## [02540] Dynamics of Fractional Order Crime Transmission Model with Fear Effect and Gang-war

**Session Date & Time**: 3E (Aug.23, 17:40-19:20)**Type**: Contributed Talk**Abstract**: Various studies present mathematical models of ordinary and fractional differential equations to reduce delinquent behavior and encourage prosocial growth. However, these models do not include the fear effect of the judiciary and of other gangs on one criminal gang, which is necessary to depict the behavioral changes of criminals. Hence, this talk will discuss a fractional-order of crime transmission model with the fear effect of the judiciary on offenders with competition effect in different gangs.**Classification**:__26A33__,__00A71__,__34A08__**Author(s)**:**Trilok Mathur**(Birla Institute of Technology and Science, Pilani)- Shivi Agarwal (Birla Institute of Technology and Science, Pilani)
- Komal Bansal (Birla Institute of Technology and Science, Pilani)

## [02607] Composition of Saigo’s k-Fractional Integral and Derivative Operators

**Session Date & Time**: 3E (Aug.23, 17:40-19:20)**Type**: Industrial Contributed Talk**Abstract**: The generalized k-fractional calculus operators generalize Saigo’s fractional integral and derivative operators, due to which many authors called this a general operator. In this paper, we established some results of the Saigo’s k-fractional integral and derivative operators involving k-hypergeometric function in the kernel are applied and established some new compositions of these operators on the k-Struve function as image formula.**Classification**:__26A33__,__33C65__,__33C20__**Author(s)**:**Sunita Nagar**(Mewar University)

## [02621] Effect of magnetic field on natural convection through infinite plates with ramped velocity

**Session Date & Time**: 3E (Aug.23, 17:40-19:20)**Type**: Industrial Contributed Talk**Abstract**: In this talk , we found the analytical solution of unsteady free convective flow of an electrically conducting and viscous incompressible fluid between two infinite parallel plates when one plate moves with a ramped velocity. An applied Magnetic field has been taken into consideration. Laplace transform techniques were used to find the non-dimensional governing equations analytically. The effect of various values for magnetic field magnetic parameter, Grashof number and time parameter are demonstrated graphically.**Classification**:__26A33__,__33C65__,__33C20__**Author(s)**:**Sangeeta Kumari**(Chandigarh University)- Vanita Vatsa (Depaertment of Mathematics, DCRUST, Murthal, INDIA)

## [01966] Fekete-Szegö Inequality for Universally Prestarlike Functions By a Variational Method

**Session Date & Time**: 3E (Aug.23, 17:40-19:20)**Type**: Contributed Talk**Abstract**: The universally prestarlike functions of order α ≤ 1 in the slit domain Λ = C [1;∞) have been recently introduced by S. Ruscheweyh. This notion generalizes the corresponding one for functions in the unit disk Δ (and other circular domains in C). In this paper, we obtain the Fekete-Szegö inequality for such functions by using Variational Method. We conclude that this paper presents a new class of functions analytic in the slit domain, and closely related to the class of starlike functions. Besides being an introduction to this field, it provides an interesting connections defined class with well-known classes. The paper deals with several ideas and techniques used in geometric function theory.**Classification**:__30C45__**Author(s)**:**Lourthu Mary Joseph**(Yuvabharathi International School)