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On asymptotic stable solutions of a quadratic Erdélyi-Kober fractional functional integral equation with linear modification of the arguments. (English) Zbl 1495.45007

MSC:

45M05 Asymptotics of solutions to integral equations
45G10 Other nonlinear integral equations
26A33 Fractional derivatives and integrals
47H08 Measures of noncompactness and condensing mappings, \(K\)-set contractions, etc.
47N20 Applications of operator theory to differential and integral equations
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[1] Doi, K.; Shimizu, S., Explicit solutions for a system of nonlinear Schrdinger equations with delta functions as initial data, Differ Integral Equ, 32, 359-367 (2019) · Zbl 1424.35312
[2] Heo, K.-u.; Koo, W.; Park, I.-K.; Ryue, J., Quadratic strip theory for high-order dynamic behavior of a large container ship with 3D flow effects, Int J Naval Archit Ocean Eng, 8, 127-136 (2016)
[3] Alias, I. A.; Huseyin, N.; Huseyin, A., Compactness of the set of trajectories of the control system described by a Urysohn type integral equation with quadratic integral constraints on the control functions, J Inequal Appl, 2016, Article 36 pp. (2016) · Zbl 1334.45010
[4] Owyed, S.; Abdou, M. A.; Abdel-Aty, A.; Ray, S. S., New optical soliton solutions of nolinear evolution equation describing nonlinear dispersion, Commun Theor Phys, 71, 1063-1068 (2019)
[5] Ismail, G. M.; Abdl-Rahim, H. R.; Abdel-Aty, A.; Kharabsheh, R.; Alharbi, W.; Abdel-Aty, M., An analytical solution for fractional oscillator in a resisting medium, Chaos Solitons Fractals, 130, 109395 (2020)
[6] Patra, A., On comparison of two reliable techniques for the Riesz fractional complex Ginzburg-Landau-Schrodinger equation in modelling superconductivity, Progr Fract Differ Appl, 5, 125-141 (2019)
[7] Shah, K.; Zeb, S.; Khan, R. A., Multiplicity results of multi-point boundary value problem of nonlinear fractional differential equations, Appl Math Inf Sci, 12, 727-734 (2018)
[8] Anastassiou, G. A.; Argyros, I. K., Iterative methods and their applications to Banach space valued functions in abstract fractional calculus, Progr Fract Differ Appl, 4, 35-47 (2018)
[9] Abdelhakem, M.; Ahmed, A.; El-kady, M., Spectral monic chebyshev approximation for higher order differential equations, Math Sci Lett, 8, 11-17 (2019)
[10] Kirk, A.; Sims, B., Handbook of metric fixed point theory (2001), Springer: Springer Berlin · Zbl 0970.54001
[11] Long, H. V.; Son, N. T.K.; Rodrguez-LpezSome, R., Generalizations of fixed point theorems in partially ordered metric spaces and applications to partial differential equations with uncertainty, Vietnam J Math, 46, 531-555 (2018) · Zbl 1497.54051
[12] Su, Y.; PetruÅel, A.; Yao, J.-C., Multivariate fixed point theorems for contractions and nonexpansive mappings with applications, Fixed Point Theory Appl, 2016, Article 9 pp. (2016)
[13] Subrahmanyam, P. V., Schauder’S fixed point theorem and allied theorem, Elem Fixed Point Theorems Springer-Nature, 245-275 (2019)
[14] Banaś, J.; Rzepka, B., On existence and asymptotic stability of a nonlinear integral equation, J Math Anal Appl, 284, 165-173 (2003) · Zbl 1029.45003
[15] Benchohra, M.; Darwish, M. A., On unique solvability of quadratic integral equations with linear modification of the argument, Miskolc Math Notes, 10, 3-10 (2009) · Zbl 1199.45013
[16] Darwish, M. A.; Henderson, J.; O’Regan, D., Existence and asymptotic stability of solutions of a perturbed fractional functional-integral equation with linear modification of the argument, Bull Korean Math Soc, 48, 539-553 (2011) · Zbl 1220.45011
[17] Art. ID 192542. · Zbl 1293.45010
[18] Darwish, M. A.; Samet, B., On Erdélyi-Kober quadratic functional-integral equation in Banach algebra, Numer Funct Anal Optim, 39, 276-294 (2018) · Zbl 1390.45010
[19] Deimling, K., Nonlinear functional analysis (1985), Springer-Verlag: Springer-Verlag Berlin, Germany · Zbl 0559.47040
[20] Stuart, C. A., Existence theorems for a class of nonlinear integral equations, Math Z, 137, 49-66 (1974) · Zbl 0289.45013
[21] Banaś, J.; Sadarangani, K., Solutions of some functional-integral equations in Banach algebra, Math Comput Model, 38, 245-250 (2003) · Zbl 1053.45007
[22] Banaś, J.; O’Regan, D., On existence and local attractivity of solutions of a quadratic integral equation of fractional order, J Math Anal Appl, 345, 573-582 (2008) · Zbl 1147.45003
[23] Caballero, J.; Rocha, J.; Sadarangani, K., On monotonic solutions of an integral equations of Volterra type, J Comput Appl Math, 174, 119-133 (2005) · Zbl 1063.45003
[24] Caballero, J.; Darwish, M. A.; Sadarangani, K., A perturbed quadratic equation involving Erdélyi-Kober fractional integral, Rev R Acad Cienc Exactas Fs Nat Ser-A Math RACSAM, 110, 541-555 (2016) · Zbl 1357.45004
[25] Darwish, M. A., On quadratic integral equation of fractional orders, J Math Anal Appl, 311, 112-119 (2005) · Zbl 1080.45004
[26] Darwish, M. A., On existence and asymptotic behaviour of solutions of a fractional integral equation, Appl Anal, 88, 169-181 (2009) · Zbl 1172.45001
[27] Darwish, M. A.; Sadarangani, K., On Erdélyi-Kober type quadratic integral equation with linear modification of the argument, Appl Math Comput, 238, 30-42 (2014) · Zbl 1334.45007
[28] Darwish, M. A.; Sadarangani, K., On a quadratic integral equation with supremum involving Erdélyi-Kober fractional order, Math Nachr, 228, 566-576 (2015) · Zbl 1316.45005
[29] Darwish, M. A., On Erdélyi-Kober fractional Urysohn-Volterra quadratic integral equations, Appl Math Comput, 273, 562-569 (2016) · Zbl 1410.45007
[30] Darwish, M. A.; Graef, J. R.; Sadarangani, K., On Urysohn-Volterra fractional quadratic integral equations, J Appl Anal Comput, 8, 331-343 (2018)
[31] Alamo, J. A.; Rodríguez, J., Operational calculs for modified Erdélyi-Koberoperators, Serdica, 20, 351-363 (1994) · Zbl 0828.44006
[32] Hilfer, R., Applications of fractional calculus in physics (2000), World Scientific: World Scientific Singapore · Zbl 0998.26002
[33] Kiryakova, V. S., Generalized fractional calculus and applications, Pitman Research Notes in Mathematics (1994), Longman: Longman NewYork · Zbl 0882.26003
[34] Mainardi, F., Fractional calculus: some basic problems in continuum and statistical mechanics, Vienna: fractals and fractional calculus in continuum mechanics (Udine, 1996), CISM courses and lectures, 378, 291-348 (1997) · Zbl 0917.73004
[35] Pagnini, G., Erdélyi-Kober fractional diffusion, Fract Calc Appl Anal, 15, 117-127 (2012) · Zbl 1276.26021
[36] Kiryakova, V. S.; Al-Saqabi, B. N., Transmutation method for solving Erdélyi-Koberfractional differintegral equations, J Math Anal Appl, 211, 347-364 (1997) · Zbl 0879.45005
[37] Argyros, I. K., Quadratic equations and applications to Chandrasekhar’s and related equations, Bull Austral Math Soc, 32, 275-292 (1985) · Zbl 0607.47063
[38] Boffi, V. C.; Spiga, G., An equation of hammerstein type arising in particle transport theory, J Math Phys, 24, 1625-1629 (1983) · Zbl 0526.45009
[39] Boffi, V. C.; Spiga, G., Nonlinear removal effects in time-dependent particle transport theory, Z Angew Math Phys, 34, 347-357 (1983) · Zbl 0528.76082
[40] Case, K. M.; Zweifel, P. F., Linear transport theory (1967), Addison-Wesley: Addison-Wesley Reading, MA, USA · Zbl 0162.58903
[41] Chandrasekhar, S., Radiative transfer (1950), Oxford University Press: Oxford University Press London, UK
[42] Hu, S.; Khavani, M.; Zhuang, W., Integral equations arising in the kinetic theory of gases, Appl Anal, 34, 261-266 (1989) · Zbl 0697.45004
[43] Kelley, C. T., Approximation of solutions of some quadratic integral equations in transport theory, J Integral Equ, 4, 221-237 (1982) · Zbl 0495.45010
[44] Leggett, R. W., A new approach to the h-equation of Chandrasekhar, SIAM J Math Anal, 7, 542-550 (1976) · Zbl 0331.45012
[45] Spiga, G.; Bowden, R. L.; Boffi, V. C., On the solutions of a class of nonlinear integral equations arising in transport theory, J Math Phys, 25, 3444-3450 (1984) · Zbl 0567.45008
[46] Banaś, J.; Goebel, K., Measures of noncompactness in Banach spaces, Lecture notes in pure and applied mathematics (1980), Marcel Dekker: Marcel Dekker New York, USA · Zbl 0441.47056
[47] Appell, J.; Banaś, J.; Merentes, N., Measures of noncompactness in the study of asymptotically stable and ultimately nondecreasing solutions of integral equations, Z Anal Anwend, 29, 251-273 (2010) · Zbl 1214.47044
[48] Appell, J.; Zabrejko, P. P., Nonlinear superposition operators (1990), Cambridge University Press: Cambridge University Press Cambridge, UK · Zbl 0701.47041
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