An existence theorem for a general class of weakly singular integral equations in Banach spaces

[1] M.S. Abod, T. Abdeljawad, S.M. Ali, and K. Shah, On fractional boundary value problems involving fractional derivatives with Mittag-Leffler kernel and nonlinear integral conditions, Adv. Contin. Discrete Mod. 37 (2021), 1–21.

[2] R.R. Akhmerov, M.I. Kamenskii, A.S. Potapov, A.E. Rodkina, and B.N. Sadovskii, Measures of Noncompactness and Condensing Operators, Birkhauser, Basel, Switzerland, 1992.

[3] H.V.S. Chauhan, B. Singh, C. Tunc, and O. Tunc, On the existence of solutions of non-linear 2D Volterra integral equations in a Banach space, Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat. 116 (2022), no. 3, 101.

[4] G. Darbo, Punti uniti in trasformazioni a codominio non compatto, Rend. Sem. Mater. Univ. Padova 24 (1955), 84–92.

[5] A. Das, B. Hazarika, S.K. Panda, and V. Vijayakumar, An existence result for an infinite system of implicit fractional integral equations via generalized Darbo’s fixed point theorem, Comput. Appl. Math. 40 (2021), no. 4, 143.

[6] A. Das, B. Hazarika, V. Parvaneh, and M. Mursaleen, Solvability of generalized fractional order integral equations via measures of noncompactness, Math. Sci. 15 (2021), 241–251.

[7] A. Deep, S. Abbas, B. Sing, M.R. Alharthi, and K.S. Nisar, Solvability of functional stochastic integral equations via Darbo’s fixed point theorem, Alexandria Engin. J. 60 (2021), no. 6, 5631–5636.

[8] A. Dehici and N. Redjel, Measure of noncompactness and application to stochastic differential equations, Adv. Differ. Equ. 28 (2016), 1–17.

[9] L.S. Goldenstein and A.S. Markus, On the measure of non-compactness of bounded sets and of linear operators, Studies in Algebra and Math. Anal. (Russian), pages 45-54, Izdat. ”Moldovenjaske”, Kishinev, 1965.

[10] M. Kazemi and R. Ezzati, Existence of solutions for some nonlinear two dimensional Volterra integral equations via measures of noncompactness, Appl. Math. Comput. 275 (2016), 165–171.

[11] M. Kazemi, R. Ezzati, and A. Deep, On the solvability of non-linear fractional integral equations of product type, J. Pseudo-Differ. Oper. Appl. 14 (2023), no. 3, 14–39.

[12] M. Kazemi, On existence of solutions for some functional integral equations in Banach algebra by fixed point theorem, Int. J. Nonlinear Anal. Appl., 13 (2022), no. 1, 451–466.

[13] K. Kuratowski, Sur les espaces completes, Fund. Math. 15 (1934), 301–335.

[14] M. Metwali and K. Cicho’n, On solutions of some delay Volterra integral problems on a half line, Nonlinear Anal.: Model. Control 26 (2021), no. 4, 661–677.

[15] R. Miller, Nonlinear Volterra Integral Equations, W.A. Benjamin, California, 1971.

[16] H. Nashine, R. Arab, and R. Agarwal, Existence of solutions of system of functional integral equations using measure of noncompactness, Int. J. Nonlinear Anal. 12 (2021), 583–595.

[17] R. Nussbaum, The fixed point index and fixed point theorems for k-set contractions, Doctoral dissertation, University of Chicago, 1969.

[18] W.V. Petryshyn, Structure of the fixed points sets of k-set contractions, Arch. Rational Mech. Anal. 40 (1971), 312–328.

[19] K. Shah, B. Abdalla, and T. Abdeljawad, Analysis of multipoint impulsive problem of fractional-order differential equations, Boundary Value Prob. 2023 (2023), no. 1, 1–17.

[20] K. Shah, T. Abdeljawad, and B. Ahmed Abdalla, On a coupled system under coupled integral boundary conditions involving non-singular differential operator, AIMS Math 8 (2023), no. 4, 9890–9910.

[21] S. Singh, S. Kumar, M.M. A. Metwali, S.F. Aldosary, and K.S. Nisar, An existence theorem for nonlinear functional Volterra integral equations via Petryshyn’s fixed point theorem, Aims Math. 7 (2022), no. 4, 5594–5604.

[22] A. Ullah, Z. Ullah, T. Abdeljawad, Z. Hammouch, and K. Shah, A hybrid method for solving fuzzy Volterra integral equations of separable type kernels, J. King Saud University-Sci. 33 (2021), no. 1, 101246.