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176 results on '"Raheem, Abdur"'

1. Time-discretization method for a multi-term time fractional differential equation with delay

Author

Khatoon, Areefa, Raheem, Abdur, and Afreen, Asma

Subjects
Mathematics - Numerical Analysis, Mathematics - Dynamical Systems, 34G20, 26A33, 37M15, 47H06, 34K30
Abstract

This paper discusses a multi-term time-fractional delay differential equation in a real Hilbert space. An iterative scheme for a multi-term time-fractional differential equation is established using Rothe's method. The method of semi-discretization is extended to this kind of time fractional problem with delay in the case that the time delay parameter $\nu >0$ satisfies $\nu\leq T$, where $T$ denotes the final time. We apply the accretivity of the operator $A$ in an iterative scheme to establish the existence and regularity of strong solutions to the considered problem. Finally, an example is provided to demonstrate the abstract result.

Published
2024

2. Stochastic controllability for a non-autonomous fractional neutral differential equation with infinite delay in abstract space

Author

Khatoon, Areefa, Raheem, Abdur, and Afreen, Asma

Subjects
Mathematics - Optimization and Control, 26A33, 93B05, 34K05, 34K35, 47H08
Abstract

This paper deals with the controllability for a class of non-autonomous neutral differential equations of fractional order with infinite delay in an abstract space. The semi-group theory of bounded linear operators, fractional calculus, and stochastic analysis techniques have been implemented to achieve the main result. We prove the existence of mild solution and controllability of the system by using the theory of measure of non-compactness, fixed point theorems, and $k$-set contractive mapping. An example is given to demonstrate the effectiveness of the abstract result.

Published
2024

3. Controllability of a second-order impulsive neutral differential equation via resolvent operator technique

Author

Afreen, Asma, Raheem, Abdur, and Khatoon, Areefa

Subjects
Mathematics - Dynamical Systems
Abstract

This paper uses the resolvent operator technique to investigate second-order non-autonomous neutral integrodifferential equations with impulsive conditions in a Banach space. We study the existence of a mild solution and the system's approximate controllability. The semigroup and resolvent operator theory, graph norm, and Krasnoselskii's fixed point theorem are used to demonstrate the results. Finally, we present our findings with an example.

Published
2023

21. Controllability of a Second-Order Impulsive Neutral Differential Equation via Resolvent Operator Technique.

Author

Afreen, Asma, Raheem, Abdur, and Khatoon, Areefa

Subjects
*RESOLVENTS (Mathematics), *IMPULSIVE differential equations, *INTEGRO-differential equations, *OPERATOR theory, *BANACH spaces
Abstract

This paper uses the resolvent operator technique to investigate second-order non-autonomous neutral integrodifferential equations with impulsive conditions in a Banach space. We study the existence of a mild solution and the system's approximate controllability. The semigroup and resolvent operator theory, graph norm, and Krasnoselskii's fixed point theorem are used to demonstrate the results. Finally, we present our findings with an example. [ABSTRACT FROM AUTHOR]

Published
2024

30. Oscillation and asymptotic behavior for fourth order neutral differential equations with mixed deviating arguments.

Author

Raheem, Abdur, Afreen, Asma, and Khatoon, Areefa

Subjects
OSCILLATION theory of difference equations, ASYMPTOTIC distribution, MATHEMATICS theorems, SUBSTITUTIONS (Mathematics), VARIATIONAL inequalities (Mathematics)
Abstract

This paper aims to study the oscillatory nature of solutions for fourth-order neutral differential equations with mixed deviating arguments and improved oscillation conditions obtained in various cases. We reduced the problem to first-order differential inequality by using suitable substitutions that enabled us to use comparison theorems. Further, we discuss the asymptotic nature of solutions, and in the end, an example is given to validate the results. [ABSTRACT FROM AUTHOR]

Published
2023

31. Efficient energy flow criteria of hybrid solar battery packs grid for electric vehicle rapid-charging facility

Author

Arfeen, Zeeshan A., Abdullah, Md Pauzi, Sheikh, Usman Ullah, Siddique, Abubakar, Raheem, Abdur, and Kausar, Mehreen

Abstract

Rapid growth in electrical transportation and a shift towards clean energy from distributed renewable energy sources are sustainable options to crack down on the demand and usage of electricity. In this paper, grid-assisted electric vehicle (EV) rapid charging facilities empowered by photovoltaic modules and battery stacks are utilised. Further, an effective interactive mechanism between EV and renewable power sources to improve system reliability – 15 efficient modes of charging are employed for the grid-connected charging station. Moreover, for long run of the charging facility, sizing components of the EV charging facilities are optimised by meta-heuristic barebones Harris hawk optimisation with a net profit of US 0.0084/kWh in criteria of no profit/loss. This is also confirmed by the swarm-style memetic grasshopper optimisation algorithm and multifarious particle swarm optimisation.

Published
2023
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32. Performance analysis of biogas net metering with the grid-connected station

Author

Shakoor, Rabia, Hameed, Sawera, Raheem, Abdur, Rashid, Muhammad, and Arfeen, Zeeshan A.

Abstract

Energy demand in Pakistan has increased surprisingly for a few years. The current generation of Pakistan is mainly reliant on thermal (fossil fuels) and crude oils. Pakistan is facing an energy gap of 5000–6000 MW between the demand and supply chain. The difference in Energy demand and energy generation for Pakistan  is major causes of power system blackouts, power tripping, and load shedding problem. This entity intrigues the government of Pakistan to open the door for Alternative Energy Sources (AES) i.e. biogas, wind and solar, etc. Biogas becomes a vital source of energy because of technological evolution, free source, environmental friendly, consumer insistence and different state policies. Integration of biogas generation through Net Metering (N-M) with electricity grid at different levels (domestic, commercial and industrial level) can minimize the energy deficiency. Present research investigates the biogas Net Metering in Pakistan. Analysis has been performed through ETAP software. It is observed that the primary burdened bus 21 has a 98.76% voltage level in Case 2, while in Case 1 the voltage profile of Bus 21 is 97.78%. Results show the contribution of Distributed Generation (DG) system in the reduction of power deficit and burden on the utility grid.

Published
2023
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41. A study of nonlocal fractional delay differential equations with hemivariational inequality.

Author

Algehyne, Ebrahem A., Raheem, Abdur, Adnan, Mohd, Afreen, Asma, and Alamer, Ahmed

Subjects
CAPUTO fractional derivatives, BANACH spaces, COSINE function, FRACTIONAL differential equations, DELAY differential equations, MONOTONE operators, SURJECTIONS
Abstract

In this paper, we study an abstract system of fractional delay differential equations of order [Math Processing Error] 1 < q < 2 with a hemivariational inequality in Banach spaces. To establish the existence of a solution to the abstract inequality, we employ the Rothe technique in conjunction with the surjectivity of multivalued pseudomonotone operators and features of the Clarke generalized gradient. Further, to show the existence of the fractional differential equation, we use the fractional cosine family and fixed point theorem. Finally, we include an example to elaborate the effectiveness of the findings. [ABSTRACT FROM AUTHOR]

Published
2023
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