Existence results for fractional neutral integro-differential systems with nonlocal condition through resolvent operators

Mallika, D.; Baleanu, D.; Suganya, S.; Arjunan, M. Mallika

doi:10.2478/auom-2019-0006

Abstract

The manuscript is primarily concerned with the new existence results for fractional neutral integro-differential equation (FNIDE) with nonlocal conditions (NLCs) in Banach spaces. Based on the Banach contraction principle and Krasnoselskii fixed point theorem (FPT) joined with resolvent operators, we develop the main results. Ultimately, an representation is also offered to demonstrate the accomplished theorem.

References

[1] J. Pruss, Evolutionary Integral Equations and Applications: Monographs in Mathematics, Vol. 87. Birkhauser, Basel, 1993.10.1007/978-3-0348-8570-6
Search in Google Scholar Back to article
[2] Y. Zhou, Basic Theory of Fractional Differential Equations, World Scientific, Singapore, 2014.10.1142/9069
Search in Google Scholar Back to article
[3] D. Baleanu, J. A. T. Machado and A. C. J. Luo, Fractional Dynamics and Control, Springer, New York, USA, 2012.10.1007/978-1-4614-0457-6
Search in Google Scholar Back to article
[4] A.A. Kilbas, H.M. Srivastava and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier, Amesterdam, 2006.
Search in Google Scholar Back to article
[5] I. Podlubny, Fractional Differential Equations, Academic Press, New York, 1999.
Search in Google Scholar Back to article
[6] B.B. Mandelbrot, The Fractal Geometry of Nature, First Edition., W. H. Freeman & Co. Ltd., New York, 1974.
Search in Google Scholar Back to article
[7] S.K. Agrawal, H.M. Srivastava and S. Das, Synchronization of fractional order chaotic systems using active control method, Chaos Solitons Fractals, 45(2012) 737–752.10.1016/j.chaos.2012.02.004
Search in Google Scholar Back to article
[8] D. Guyomar, B. Ducharne, G. Sebald and D. Audiger, Fractional derivative operators for modeling the dynamic polarization behavior as a function of frequency and electric field amplitude, IEEE Trans. Ultrason. Ferroelectr. Freq. Control, 56(2009), 437–443.10.1109/TUFFC.2009.106219411204
Search in Google Scholar Back to article
[9] I.S. Jesus and J.A.T. Machado, Implementation of fractional-order electromagnetic potential through a genetic algorithm, Commun. Nonlinear Sci. Numer. Simul., 14(2009), 1838–1843.10.1016/j.cnsns.2008.08.015
Search in Google Scholar Back to article
[10] F.C. Meral, T.J. Royston and R. Magin, Fractional calculus in viscoelasticity: An experimental study, Commun. Nonlinear Sci. Numer. Simul., 15(2010), 939–945.10.1016/j.cnsns.2009.05.004
Search in Google Scholar Back to article
[11] M.D. Ortigueira, C.M. Ionescu, J.T. Machado and J.J. Trujillo, Fractional signal processing and applications, Signal Process, 107(2015) 197–197.10.1016/j.sigpro.2014.10.002
Search in Google Scholar Back to article
[12] F. Wang, D. Chen, X. Zhang and Y. Wub, The existence and uniqueness theorem of the solution to a class of nonlinear fractional order system with time delay, Applied Mathematics Letters, 53(2016), 45-51.10.1016/j.aml.2015.10.001
Search in Google Scholar Back to article
[13] E. Hernandez, D.O’ Regan and K. Balachandran, On recent developments in the theory of abstract differential equations with fractional derivatives, Nonlinear Anal., 73(2010), 3462–3471.10.1016/j.na.2010.07.035
Search in Google Scholar Back to article
[14] E. Hernandez and H.R. Henriquez, Impulsive partial neutral differential equations, Applied Mathematical Letters, 19(2006), 215–222.10.1016/j.aml.2005.04.005
Search in Google Scholar Back to article
[15] J. K. Hale and S. M. Verduyn Lunel, Introduction to Functional-Differential Equations, Springer-Verlag, New York, 1993.10.1007/978-1-4612-4342-7
Search in Google Scholar Back to article
[16] L. Byszewski, Theorems about existence and uniqueness of solutions of a semi-linear evolution nonlocal Cauchy problem, J. Math. Anal. Appl., 162(1991), 494–505.10.1016/0022-247X(91)90164-U
Search in Google Scholar Back to article
[17] L. Byszewski and V. Lakshmikantham, Theorem about the existence and uniqueness of a solution of a nonlocal abstract Cauchy problem in a Banach space, Appl. Anal., 40(1991), 11–19.10.1080/00036819008839989
Search in Google Scholar Back to article
[18] Y. Zhou and F. Jiao, Existence of mild solutions for fractional neutral evolution equations, Comput. Math. Appl., 59(3)(2010), 1063–1077.10.1016/j.camwa.2009.06.026
Search in Google Scholar Back to article
[19] K. Balachandran and S. Kiruthika, Existence results for fractional integrodifferential equations with nonlocal condition via resolvent operators, Computers and Mathematics with Applications, 62(2011), 1350–1358.10.1016/j.camwa.2011.05.001
Search in Google Scholar Back to article
[20] S. Suganya, D. Baleanu and M. Mallika Arjunan, A note on fractional neutral integro-differential inclusions with state-dependent delay in Banach spaces, Journal of Computational Analysis & Applications, 20(1)(2016), 1302–1317.
Search in Google Scholar Back to article
[21] P. Balasubramaniam and P. Tamilalagan, Approximate controllability of a class of fractional neutral stochastic integro-differential inclusions with infinite delay by using Mainardi function, Applied Mathematics and Computation, 256(2015), 232–2466.10.1016/j.amc.2015.01.035
Search in Google Scholar Back to article
[22] X.B. Shu and F. Xu, The existence of solutions for impulsive fractional partial neutral differential equations, Journal of Mathematics, Volume 2013, Article ID 147193, 9 pages.10.1155/2013/147193
Search in Google Scholar Back to article

Existence results for fractional neutral integro-differential systems with nonlocal condition through resolvent operators

Abstract

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