A novel numerical technique and stability criterion of VF type integro-differential equations of non-integer order

Document Type : Research Paper


1 Department of Mathematics, National Institute of Technology Silchar, Assam, India

2 Department of Mechanical Engineering, National Institute of Technology Silchar, Assam, India


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.


[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.
Volume 13, Special Issue for selected papers of ICDACT-2021
The link to the conference website is https://vitbhopal.ac.in/event/icdact_dec_21/
March 2022
Pages 133-145
  • Receive Date: 15 August 2021
  • Revise Date: 22 December 2021
  • Accept Date: 15 January 2022