Browsing by Author "Ahsan, Sumbal"

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Analytical Solution of System of Volterra Integral Equations Using OHAM
(2020) Baleanu, Dumitru; Nawaz, Rashid; Ahsan, Sumbal; Baleanu, Dumitru; Nisar, Kottakkaran Sooppy; 56389
In this work, a reliable technique is used for the solution of a system of Volterra integral equations (VIEs), called optimal homotopy asymptotic method (OHAM). The proposed technique is successfully applied for the solution of different problems, and comparison is made with the relaxed Monto Carlo method (RMCM) and hat basis function method (HBFM). The comparisons show that the present technique is more suitable and reliable for the solution of a system of VIEs. The presented technique uses auxiliary function containing auxiliary constants, which control the convergence. Moreover, OHAM does not require discretization like other numerical methods and is also free from small or large parameter.
Approximate solutions of nonlinear two-dimensional Volterra integral equations
(2021) Baleanu, Dumitru; Nawaz, Rashid; Akbar, Muhammad; Nisar, Kottakkaran Sooppy; Baleanu, Dumitru; 56389
The present work is concerned with examining the Optimal Homotopy Asymptotic Method (OHAM) for linear and nonlinear two-dimensional Volterra integral equations (2D-VIEs). The result obtained by the suggested method for linear 2D-VIEs is compared with the differential transform method, Bernstein polynomial method, and piecewise block-plus method and result of the proposed method for nonlinear 2D-VIEs is compared with 2D differential transform method. The proposed method provides us with efficient and more accurate solutions compared to the other existing methods in the literature.
New iterative approach for the solutions of fractional order inhomogeneous partial differential equations
(2021) Baleanu, Dumitru; Nawaz, Rashid; Ahsan, Sumbal; Nisar, Kottakkaran Sooppy; Baleanu, Dumitru; 56389
In this paper, the study of fractional order partial differential equations is made by using the reliable algorithm of the new iterative method (NIM). The fractional derivatives are considered in the Caputo sense whose order belongs to the closed interval [0,1]. The proposed method is directly extended to study the fractional-order Roseau-Hyman and fractional order inhomogeneous partial differential equations without any transformation to convert the given problem into integer order. The obtained results are compared with those obtained by Variational Iteration Method (VIM), Homotopy Perturbation Method (HPM), Laplace Variational Iteration Method (LVIM) and the Laplace Adominan Decomposition Method (LADM). The results obtained by NIM, show higher accuracy than HPM, LVIM and LADM. The accuracy of the proposed method improves by taking more iterations. © 2021 the Author(s), licensee AIMS Press.