Wang, JinRong; Zhu, Chun; Fečkan, Michal Solvability of fully nonlinear functional equations involving Erdélyi-Kober fractional integrals on the unbounded interval. (English) Zbl 1296.45004 Optimization 63, No. 8, 1235-1248 (2014). Summary: In this paper, we study the existence of solutions to fully nonlinear functional equations involving Erdélyi-Kober fractional integrals on the unbounded interval. By constructing a closed and convex subset of a Fréchet space, sufficient conditions are presented by using a fixed point theorem via the Kuratowski measure. Finally, an example is given to illustrate the obtained result. Cited in 7 Documents MSC: 45G05 Singular nonlinear integral equations 47H30 Particular nonlinear operators (superposition, Hammerstein, Nemytskiĭ, Uryson, etc.) 26A33 Fractional derivatives and integrals Keywords:nonlinear functional equation; Erdélyi-Kober fractional integrals; unbounded interval; solvability PDFBibTeX XMLCite \textit{J. Wang} et al., Optimization 63, No. 8, 1235--1248 (2014; Zbl 1296.45004) Full Text: DOI References: [1] Olszowy L, Dyn. Sys. Appl 18 pp 667– (2009) [2] DOI: 10.1016/j.na.2006.03.015 · Zbl 1128.45004 · doi:10.1016/j.na.2006.03.015 [3] DOI: 10.1016/j.na.2009.04.037 · Zbl 1181.45010 · doi:10.1016/j.na.2009.04.037 [4] Kilbas AA, In: North-Holland mathematics studies 204 (2006) [5] DOI: 10.1007/978-3-642-60185-9_24 · doi:10.1007/978-3-642-60185-9_24 [6] DOI: 10.1016/0888-3270(91)90016-X · doi:10.1016/0888-3270(91)90016-X [7] DOI: 10.1016/S0006-3495(95)80157-8 · doi:10.1016/S0006-3495(95)80157-8 [8] DOI: 10.1142/9789812817747 · doi:10.1142/9789812817747 [9] DOI: 10.1007/978-3-7091-2664-6_7 · doi:10.1007/978-3-7091-2664-6_7 [10] DOI: 10.1063/1.470346 · doi:10.1063/1.470346 [11] DOI: 10.1007/978-3-642-14003-7 · doi:10.1007/978-3-642-14003-7 [12] DOI: 10.1016/j.camwa.2011.03.049 · Zbl 1228.45002 · doi:10.1016/j.camwa.2011.03.049 [13] DOI: 10.1016/j.jmaa.2005.02.012 · Zbl 1080.45004 · doi:10.1016/j.jmaa.2005.02.012 [14] DOI: 10.1016/j.jmaa.2006.11.008 · Zbl 1123.45001 · doi:10.1016/j.jmaa.2006.11.008 [15] DOI: 10.1016/j.jmaa.2008.04.050 · Zbl 1147.45003 · doi:10.1016/j.jmaa.2008.04.050 [16] DOI: 10.1016/j.jmaa.2010.09.004 · Zbl 1210.45005 · doi:10.1016/j.jmaa.2010.09.004 [17] DOI: 10.1016/j.camwa.2012.03.006 · Zbl 1268.45001 · doi:10.1016/j.camwa.2012.03.006 [18] DOI: 10.2478/s11533-012-0120-9 · Zbl 1277.47067 · doi:10.2478/s11533-012-0120-9 [19] DOI: 10.1016/j.cnsns.2011.05.034 · Zbl 1257.45004 · doi:10.1016/j.cnsns.2011.05.034 [20] DOI: 10.1016/j.cnsns.2011.12.002 · Zbl 1298.45011 · doi:10.1016/j.cnsns.2011.12.002 [21] DOI: 10.2478/s11534-013-0219-z · doi:10.2478/s11534-013-0219-z [22] Olszowy L, Comment. Math 48 pp 103– (2008) [23] DOI: 10.1007/978-1-4613-1281-9 · doi:10.1007/978-1-4613-1281-9 [24] Banaś J, Measures of noncompactness in Banach spaces 60 (1980) [25] Prudnikov AP, In: Elementary functions 1 (1981) [26] Gradshteyn IS, Table of integrals, series, and products, 7. ed. (2007) [27] DOI: 10.1016/j.apm.2012.12.011 · Zbl 1305.34134 · doi:10.1016/j.apm.2012.12.011 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.