Ulam Stabilities for Nonlinear Volterra Delay Integro-differential Equations

L. Cadariu, V. Radu, “On the stability of the Cauchy functional equation: a fixed point approach”, Grazer Math. Ber., 346, 43–52, 2004.

L. P. Castro, R. C. Guerra, “Hyers-Ulam-Rassias stability of Volterra integral equation within weighted spaces”, Libertas Mathematica, 33, 21–35, 2013.

L. P. Castro, A. Ramos, “Hyers-Ulam-Rassias stability for a class of nonlinear Volterra integral equations”, Banach J. Math. Anal., 3(1), 36–43, 2009.

J. P. Dauer, K. Balachandran, “Existence of solutions of nonlinear neutral integro-differential equations in Banach spaces”, Journal of Mathematical Analysis and Applications, 251, 93–105, 2000.

M. Gachpazan, O. Baghani, “Hyers-Ulam stability of nonlinear integral equation”, Fixed Point Theory and Applications, 2010, 927640–927645, 2010.

M. Gachpazan, O. Baghani, “Hyers-Ulam stability of Volterra integral equation”, Int. J. Nonlinear Anal. Appl., 1(2), 19–25, 2010.

J. Huang, Y. Li, “Hyers-Ulam stability of delay differential equations of first order”, Math. Nachr., 289(1), 60–66, 2016.

M. Janfada, G. Sadeghi, “Stability of the Volterra integro-differential equation”, Folia Mathematica, 18(1), 11–20, 2013.

S. M. Jung, “A fixed point approach to the stabilty of a Volterra integral equations”, Fixed point Theory and Applications, 2007, 57064–57073, 2007.

K. D. Kucche, P. U. Shikhare, “Ulam-Hyers Stability of integro-differential Equations in Banach Spaces via Pachpatte Inequality”, Asian-European Journal of Mathematics, 11(2), 1850062–1850081, 2018.

K. D. Kucche and M. B. Dhakne, “On existence results and qualitative properties of mild solution of semilinear mixed Volterra-Fredholm functional integro-differential equations in Banach spaces”, Appl. Math. Comput., 219, 10806–10816, 2013.

K. D. Kucche, M. B. Dhakne, “Existence of solution via integral inequality of Volferra-Predholm neutral functional integro-differential equations with infinite delay”, Int. J. Diff. Eqs., Article ID 784956, 13 pages, 2014.

J. R. Morales, E. M. Rojas, “Hyers-Ulam and Hyers-Ulam-Rassias stability of nonlinear integral equations with delay”, Int. J. Nonlinear Anal. Appl., 2(2), 1–6, 2011.

S. K. Ntouyas, “Initial and boundary value problems for functional differential equations via the topological transversality method: A survey”, Bull. Greek Math. Soc., 40, 3–41, 1998.

S. K. Ntouyas and P. Ch. Tsamatos, “Global existence for functional semilinear volterra integro-differential equations in Banach space”, Act. Math. Hungar., 80(1–2), 67–82, 1998.

D. Otrocol, “Ulam stablities of differential equations with abstract Volterra operator in a Banach space”, Nonlinear Functional Analysis and Application, 15(4), 613–619, 2010.

D. Otrocol, V. Ilea, “Ulam stablity for a delay differential equations”, Cen. Eur. J. Math., 11(7), 1296–1303, 2013.

B. G. Pachpatte, Inequalities for differential and integral equations (Academic Press, New York, 1998).

I. Rus, “Gronwall lemmas: ten open problems”, Sci. Math. Jpn., 70, 221–228, 2009.

I. Rus, “Ulam stability of ordinary differential equations”, “BABES-BOLYAI”, Mathematica, 54(4), 125–133 2009.

S. Sevgin, H. Sevli, “Stability of a nonlinear Volterra integro-differential equation via a fixed point approach”, J. Nonlinear Sci. Appl., 9, 200–207, 2016.

C. Tunc, E. Bicer, “Hyers-Ulam-Rassias stability for a first order functional differential equation”, J. Math. Fund. Sci., 47(2), 143–153, 2015.

S. M. Ulam, Problems in Modern Mathematics (John Wiley and Sons, New York, 1960).