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A novel numerical technique and stability criterion of VF type integro-differential equations of non-integer order | ||
| International Journal of Nonlinear Analysis and Applications | ||
| دوره 13، Special Issue for selected papers of ICDACT-2021، خرداد 2022، صفحه 133-145 اصل مقاله (429.65 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2022.6339 | ||
| نویسندگان | ||
| Dipankar Saha1؛ Nimai Sarkar* 1؛ Mausumi Sen1؛ Subhankar Saha2 | ||
| 1Department of Mathematics, National Institute of Technology Silchar, Assam, India | ||
| 2Department of Mechanical Engineering, National Institute of Technology Silchar, Assam, India | ||
| تاریخ دریافت: 24 مرداد 1400، تاریخ بازنگری: 01 دی 1400، تاریخ پذیرش: 25 دی 1400 | ||
| چکیده | ||
| In this article, Ulam Hyers stability of Volterra Fredholm (VF) type fractional integro-differential equation is studied by the fixed point notion in the generalized metric space. In addition, the efficiency of the Laplace decomposition method in the context of solving some integral equations of the Volterra Fredholm type is shown. Further convergence analysis of the numerical scheme is shown. | ||
| کلیدواژهها | ||
| Fixed point؛ Ulam Hyers stability؛ Metric space | ||
| مراجع | ||
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[1] Y. Atalan and V. Karakaya,Stability of nonlinear Volterra-Fredholm integro differential equation: A fixed point approach, Creat. Math. Inf. 26 (2017), 247–254. [2] A.A. Hamoud and K.P. Ghadle,The approximate solutions of fractional Volterra-Fredholm integro-differential equations by using analytical techniques, Probl. Anal. Issues Anal. 7 (2018), 41–58. [3] A.A. Hamoud and K.P. Ghadle,Usage of the homotopy analysis method for solving fractional Volterra-Fredholm integro-differential equation of the second kind, Tamkang J. Math. 49 (2018), 301–315. [4] A.A. Hamoud and K.P. Ghadle, Some new existence, uniqueness and convergence results for fractional VolterraFredholm integro-differential equations, J. Appl. Comput. Mech. 5 (2019), 58–69. [5] A.A. Hamoud, K.P. Ghadle and S. Atshan,The approximate solutions of fractional integro-differential equations by using modified Adomian decomposition method, Khayyam J. Math. 5 (2019), 21–39. [6] A.A. Hamoud, K.P. Ghadle, M.S.I. Banni and Giniswamy, Existence and uniqueness theorems for fractional Volterra-Fredholm integro-differential equations, Int. J. Appl. Math. 31 (2018), 333–348. [7] X. Ma and C. Huang, Numerical solution of fractional integro-differential equations by a hybrid collocation method, Appl. Math. Comput. 219 (2013), 6750–6760. [8] R. Mittal and R. Nigam, Solution of fractional integro-differential equations by Adomian decomposition method, Int. J. Appl. Math. Mech. 4 (2008), 87–94. [9] D. Saha, M. Sen and R.P. Agarwal, A Darbo fixed point theory approach towards the existence of a functional integral equation in a Banach algebra, Appl. Math. Comput. 358 (2019), 111–118.[10] D. Saha and M. Sen, Solution of a generalized two dimensional fractional integral equation, Int. J. Nonlinear Anal. Appl. 12 (2021), 481–492. [11] N. Sarkar and M. Sen, An investigation on existence and uniqueness of solution for integro differential equation with fractional order, J. Phys.: Conf. Ser. 1849 (2021), 012011. [12] N. Sarkar, M. Sen and D. Saha, Solution of non linear Fredholm integral equation involving constant delay by BEM with piecewise linear approximation, J. Interdiscip. Math. 33 (2020), 537–544. [13] D. Saha, M. Sen, N. Sarkar and S. Saha, Existence of a solution in the Holder space for a nonlinear functional integral equation, Armenian J. Math. 12 (2020), 1–8. [14] N. Sarkar, M. Sen and D. Saha, A new approach for numerical solution of singularly perturbed Volterra integrodifferential equation, Design Engin. 2021 (2021), 9629–9641. [15] B.C. Tripathy, S. Paul and N.R. Das, A fixed point theorem in a generalized fuzzy metric space, Bol. Sociedade Paranaense. Mat. 32 (2014), no. 2, 221–227. | ||
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