[1] M. A. Abdou, On the solution of linear and non-linear integral equation, Appl. Math. Comput. 146(2003), 857-871.
[2] G. Adomian, Solving Frontier Problem of Physics: The Decomposition Method; Kluwer Academic Press: Dordrecht the Netherlands, 1994.
[3] A. Aghajani, Y. Jalilian, Existence and global attractivity of solutions of non-linear functional integral equation, Commun. Non. Sci. Number. Simul. 15(2010), 3306-3312.
[4] I. K. Argyros, Quadratic equations and applications to Chandrasekhar and related equations, Bull. Aus. Math. Soc. 32(1985), 275-292.
[5] J. Banas, K. Goebel, Measures of Noncompactness in Banach Spaces, Marcel Dekker, New York, 1980.
[6] J. Banas, M. Lecko, Fixed points of the product of operators in Banach algebra, Panamer. Math. J. 12 (2002), 101-109.
[7] J. Banas, B. Rzepka, On existence and asymptotic stability of solutions of a nonlinear integral equation, J. Math. Anal. Appl. 284 (2003), 165-173.
[8] J. Banas, K. Sadarangani, Solutions of some functional integral equations in Banach algebra, Math. Comput. Modelling 38 (2003), 245-250.
[9] J. Biazar, H. Ghazvini, He homotopy perturbation method for solving systems of Volterra integral equations of the second kind, Cha. Solit. Frac. 39(2009), 770-777.
[10] J. Caballero, A. B. Mingarelli, K. Sadarangani, Existence of solutions of an integral equation of Chandrasekhar type in the theory of radiative transfer, Elect. J. Diff. Eqs. 57(2006), 1-11.
[11] S. Chandrasekhar, Radiative Transfer, Oxford Univ. Press, London, 1950.
[12] C. Corduneanu, Integral Equations and Applications, Cambridge University Press, New York, 1990.
[13] A Das, M Rabbani, B Hazarika, R Arab, Solvability of infinite system of nonlinear singular integral equations in the C(I × I,c) space and modified semi-analytic method to find a closed-form of solution., Int. J. Non. Anal.Appl. 10(1)(2019), 63-76.
[14] A. Deep, Deepmala, J. R. Roshan, K. S. Nisar, T. Abdeljawad, An extension of Darbo’s fixed point theorem for a class of system of nonlinear integral equations, Adv. Diff. Eqs, 2020:483(2020).
[15] A. Deep, Deepmala, R. Ezzati, Application of Petryshyn’s fixed point theorem to solvability for functional integral equations, Appl. Math. Comput. 395(2021), 125878.
[16] Deepmala, H.K.Pathak, A study on some problems on existence of solutions for some nonlinear functional integral equations, Acta. Math. Sci.33(5)(2013),1305-1313.
[17] K. Deimling, Nonlinear Functional Analysis, Springer-Verlag, 1985.
[18] B. C. Dhage, On α-condensing mappings in Banach algebras, The Math. Student 63 (1994), 146-152.
[19] B. Hazarika, H.M.Srivastava, R. Arab, M. Rabbani, Application of simulation function and measure of noncompactness for solvability of nonlinear functional integral equations and introduction to an iteration algorithm to find solution, Appl. Math. Comput. 360(2019), 131-146.
[20] J. H. He, A new approach to nonlinear partial differential equations., Comm. Nonlinear Sci. Number. Simulation 2(4)(1997), 230-235.
[21] S. Hu, M. Khavanin, W. Zhuang, Integral equations arising in the kinetic theory of gases, Appl. Anal. 34 (1989), 261-266.
[22] M. Kazemi, R. Ezzati, Existence of solutions for some nonlinear Volterra integral equations via Petryshyn’s fixed point theorem, Int. J. Anal. Appl. 9(2018).
[23] K. Maleknejad, K. Nouri, R. Mollapourasl, Existence of solutions for some nonlinear integral equations, Commun. Nonlinear Sci. Numer. Simulat. 14 (2009), 2559-2564.
[24] S.A. Mohiuddine, H.M. Srivastava, A. Alotaibi, Applications of measures of noncompactness to the infinite system of second order differential equations in lp spaces, Adv. Differ. Equ. 2016(2016), 1-13.
[25] M. Mursaleen, S.A. Mohiuddine, Applications of noncompactness to the infinite system of differential equations in lp spaces, Nonlinear Anal. 4(2012), 2111-2115.
[26] R.D. Nussbaum, The fixed point index and fixed point theorem for k set contractions, Proquest LLC, Ann Arbor, MI, 1969. Thesis(Ph.D)- The University of Chicago.
[27] D. O’Regan, Existence results for nonlinear integral equations, J. Math. Anal. Appl. 192(1995), 705-726.
[28] I. Ozdemir, U. Cakan, B. Iihan, On the existence of the solution for some nonlinear Volterra integral equations, Abstr. Appl. Anal. 5(2013).
[29] W.V. Petryshyn, Structure of the fixed points sets of k-set-contractions, Arch. Rational Mech. Anal., 40(1970-1971), 312-328.
[30] M. Rabbani, An iterative algorithm to find a closed form of solution for Hammerstein nonlinear integral equation constructed by the concept of cosm-rs, Mathematical Sciences 13 (3), (2019)299-305.
[31] B. Hazarik, M. Rabbani, RP. Agarwal, A. Das, R. Arab, Existence of Solution for Infinite System of Nonlinear Singular Integral Equations and Semi-Analytic Method to Solve it., Iranian Journal of Science and Technology, Transactions A: Science 45(2021), 235-245.
[32] M. Rabbani, A. Gelayeri, Computation Adomian Method for Solving Non-linear Differential Equation in the Fluid Dynamic., Int. J. Mechat., Elect. Compu. Techn. 5(14)(2015), 2039-2043.
[33] J. R. Roshan, Existence of solutions for a class of system of functional integral equation via measure of noncompactness J. Comput. Appl. Math. 313(2017), 129-141.
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