Analyzing the existence of solution of a fractional order integral equation: A fixed point approach

• Autorzy: Saha, Dipankar , Sen, Mausumi , Roy, Santanu
• Języki publikacji: EN

Abstrakty

EN

This paper signifies the beauty of fixed point theory in the context of attaining the sufficient condition for the existence of the solution of a non-linear functional-integral equation in an unbounded interval. Here a non-linear integral equation (NLIE) involving a fractional operator is taken in the form of an operator equation. Utilizing the perception of measure of noncompactness (MNC) along with certain relevant assumptions, it is proved that the operator equation satisfies the Darbo condition for the product of operators in a Banach algebra. Finally, the result obtained is verified by the assistance of the numerical example.

Słowa kluczowe

EN

functional-integral equation; Banach algebra; measure of noncompactness

• Czasopismo: Journal of Applied Analysis
• Rocznik: 2022
• Tom: Vol. 28, nr 2
• Strony: 199--210
• Opis fizyczny: Bibliogr. 23 poz.

Twórcy

autor

Saha, Dipankar

• National Institute of Technology Silchar, Silchar, India,

autor

Sen, Mausumi

• National Institute of Technology Silchar, Silchar, India,

autor

Roy, Santanu

• National Institute of Technology Silchar, Silchar, India,

Bibliografia

• [1] A. Aghajani and M. Aliaskari, Measure of noncompactness in banach algebra and application to the solvability of integral equations in BC(R₊, Inf. Sci. Lett. 192 (2015), 93-99.
• [2] I. K. Argyros, Quadratic equations and applications to Chandrasekhar’s and related equations, Bull. Aust. Math. Soc. 32 (1985), no. 2, 275-292.
• [3] J. Banaś and K. Goebel, Measures of Noncompactness in Banach Spaces, Lecture Notes Pure Appl. Math. 60, Marcel Dekker, New York, 1980.
• [4] T. A. Burton and B. Zhang, Fixed points and stability of an integral equation: nonuniqueness, Appl. Math. Lett. 17 (2004), no. 7, 839-846.
• [5] J. Caballero, A. B. Mingarelli and K. Sadarangani, Existence of solutions of an integral equation of Chandrasekhar type in the theory of radiative transfer, Electron. J. Differential Equations 2006 (2006), Paper No. 57.
• [6] K. M. Case and P. F. Zweifel, Linear Transport Theory, Addison-Wesley, Reading, 1967.
• [7] S. Chandrasekhar, Radiative Transfer, Dover, New York, 1960.
• [8] M. A. Darwish, On quadratic integral equation of fractional orders, J. Math. Anal. Appl. 311 (2005), no. 1, 112-119.
• [9] M. A. Darwish and K. Sadarangani, On Erdélyi-Kober type quadratic integral equation with linear modification of the argument, Appl. Math. Comput. 238 (2014), 30-42.
• [10] M. A. Darwish and B. Samet, On Erdélyi-Kober quadratic functional-integral equation in Banach algebra, Numer. Funct. Anal. Optim. 39 (2018), no. 3, 276-294.
• [11] K. Deimling, Nonlinear Functional Analysis, Springer, Berlin, 1985.
• [12] S. Hu, M. Khavanin and W. Zhuang, Integral equations arising in the kinetic theory of gases, Appl. Anal. 34 (1989), no. 3-4, 261-266.
• [13] X. Hu and J. Yan, The global attractivity and asymptotic stability of solution of a nonlinear integral equation, J. Math. Anal. Appl. 321 (2006), no. 1, 147-156.
• [14] C. T. Kelley, Approximation of solutions of some quadratic integral equations in transport theory, J. Integral Equations 4 (1982), no. 3, 221-237.
• [15] R. W. Leggett, A new approach to the H-equation of Chandrasekhar, SIAM J. Math. Anal. 7 (1976), no. 4, 542-550.
• [16] Z. Liu and S. M. Kang, Existence of monotone solutions for a nonlinear quadratic integral equation of Volterra type, Rocky Mountain J. Math. 37 (2007), no. 6, 1971-1980.
• [17] K. Maleknejad, K. Nouri and R. Mollapourasl, Existence of solutions for some nonlinear integral equations, Commun. Nonlinear Sci. Numer. Simul. 14 (2009), no. 6, 2559-2564.
• [18] L. N. Mishra, R. P. Agarwal and M. Sen, Solvability and asymptotic behavior for some nonlinear quadratic integral equation involving Erdelyi Kober fractional integrals on the unbounded interval, Progr. Fract. Diff. Appl. 2 (2016), 2559-2564.
• [19] L. N. Mishra and M. Sen, On the concept of existence and local attractivity of solutions for some quadratic Volterra integral equation of fractional order, Appl. Math. Comput. 285 (2016), 174-183.
• [20] L. N. Mishra, M. Sen and R. N. Mohapatra, On existence theorems for some generalized nonlinear functional-integral equations with applications, Filomat 31 (2017), no. 7, 2081-2091.
• [21] L. N. Mishra, H. M. Srivastava and M. Sen, On Existence Theorems for Some Generalized Nonlinear Functional-Integral Equations with Applications, Int. J. Anal. Appl. 11 (2016), 1-10.
• [22] D. Saha, M. Sen, N. Sarkar and S. Saha, Existence of a solution in the Holder space for a nonlinear functional integral equation, Armen. J. Math. 12 (2020), Paper No. 7.
• [23] M. Sen, D. Saha 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.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2024).

Identyfikatory

DOI

10.1515/jaa-2021-2072