Original Research Article

Article volume = 2023 and issue = 2

Pages: 103–109

Article publication Date: November 21, 2023

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Existence of a solution of the fractional integral system of equations via a measure of noncompactness

Mohammad Bagher Ghaemi and Hengameh Tamimi

Iran University of Science and Technology, Tehran, Iran.

Abstract:

This paper studies the existence of a solution for a system of fractional integral equations using Darbo's fixed point theorem under the measure of noncompactness. Moreover, some tables and figures are presented to show the efficiency of our main results. In this paper, by applying the artificial small parameter method, we approximate the solution of one example.

Keywords:

Fixed-point theorems; Integro-ordinary differential equations; Measures of noncompactness; condensing mappings.

References:
  • [1] J. Banaś, K. Goebel, Measures of noncompactness in Banach spaces, Lecture Notes in Pure and Applied Mathematics, vol. 60, Marcel Dekker, New York, (1980). 2.2
  • [2] G. Darbo, Punti uniti in trasformazioni a codominio non compatto, Rend. Sem. Mat. Univ. Padova. 24 (1955) 84-92.
  • [3] K. Kuratowski, Sur les espaces complets, Fund. Math. 15 (1930) 301-309.
  • [4] H. Tamimi, S. Saiedinezhad, M. B. Ghaemi, The measure of noncompactness in a generalized coupled fixed point theorem and its application to an integro-differential system, Journal of Computational and Applied Mathematics, 413 (2022) 114380. 1, 2.1, 2.1
  • [5] H. Tamimi, S. Saiedinezhad, M. B. Ghaemi, Study on the integro-differential equations on C1(R+). Comp. Appl. Math. 42, 93 (2023).
  • [6] A.M. Wazwaz, Linear and Nonlinear Integral Equations Methods and Applications, Springer Heidelberg Dordrecht, London, New York, 2011. 4
  • [7] A.M. Lyapunov, (1892). General problem on stability of motion. Taylor & Francis, London, 1992. (English translation). 4
  • [8] G. Adomian, Solving Frontier Problem of Physics: The Decomposition Method, Kluwer Academic Press, 1994. 4
  • [9] J.H. He, Homotopy perturbation method: A new nonlinear analytical technique, Appl. Math. Comput. 135 (1) (2003) 73-79. 4
  • [10] S. J. Liao, An approximate solution technique not depending on small parameters: a special example, Int. J. Non-Linear Mech. 30 (3) (1995) 371–380. 4
  • [11] S. Liao, Beyond perturbation: introduction to the homotopy analysis method, Chapman and Hall/CRC, 2003. 4
Cite this article as:
  • Mohammad Bagher Ghaemi and Hengameh Tamimi, Existence of a solution of the fractional integral system of equations via a measure of noncompactness, Communications in Combinatorics, Cryptography & Computer Science, 2023(2), PP.103–109, 2023
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