Existence and Stability Results for the Solution of Neutral Fractional Integro-Differential Equation with Nonlocal Conditions
Keywords:Neutral fractional integro-differential equation, Existence, Stability, nonlocal conditions, Fixed point theory
This paper deals with the existence and uniqueness results for the solution of a Neutral fractional integro-differential problem with nonlocal conditions. Using the Nonlinear alternative for single valued maps, Krasnoselskii's and Banach fixed point theorems to proof our main results. An example is given to illustrate our main results.
H. M. Srivastava A. A. Kilbas and J. J. Trujillo. Theory and Applications of Fractional Differential Equations. 204. Elsevier, North-Holland Mathematics Studies, 2006.
C. M. A. Pinto A. Carvalho. A delay fractional order model for the co-infection of malaria and HIV/AIDS. Int. J. Dyn. Control, 5:168–186, 2017.
J. Dugundji A. Gramas. Fixed Point Theory. Springer, New York, NY, USA, 2003.
M. S. Abdo and S. K. Panchal. Effect of perturbation in the solution of fractional neutral functional differential equations. Journal of the Korean Society for Industrial and Applied Mathematics, 21(1):63–74, 2018.
M. S. Abdo and S. K. Panchal. Some new uniqueness results of solutions to nonlinear frac- tional integro-differential equations. Annals of Pure and Applied Mathematics, 16(2):345– 352, 2018.
M. S. Abdo and S. K. Panchal. Weighted fractional neutral functional differential equations. J. Sib. Fed. Univ. Math. Phys., 11(5):535–549, 2018.
M. S. Abdo and S. K. Panchal. Fractional integro-differential equations involving ψ-hilfer fractional derivative. Adv. Appl. Math. Mech., 11(2): 360-380, 2019.
M. S. Abdo and S. K. Panchall. Existence and continuous dependence for fractional neutral functional differential equations. J. Mathematical Model., 5:153–170, 2017.
B. Ahmad, Y. Alruwaily, A. Alsaedi and S. K. Ntouyas Existence and stability results for a fractional order differential equation with non-conjugate Riemann-Stieltjes integro-multipoint boundary conditions. Mathematics, 249(7):1–14, 2019.
S. Salem, B. Ahmed, A. Alsaedi and S. K. Ntouyas. Fractional differential equation involving mixed nonlinearities with nonlocal multi-point and Reimann-Steiljes integral-multi-strip conditions. Fractal and Fractional journal, 34(3):1–16, 2019.
K. Balachandran and F. P. Samuel. Existence of solutions for quasilinear delay integrodif- ferential equations with nonlocal condition. Electronic J. Diff. Equ., 2009:1–7, 2009.
K. Balachandran and J. J. Trujillo. The nonlocal Cauchy problem for nonlinear fractional integro-differential equations in Banach spaces. Nonlinear Anal. Theory Meth. Applic., 72:4587–4593, 2010.
R. Hilfer. Applications of Fractional Calculus in Physics. A. World Scientific, Singapore, 2000.
C. P. Lia nd F. R. Zhang. A survey on the stability of fractional differential equations. European Physical Journal, Special Topics, 193:27–47, 2011.
H. A. Wahach, S. K. Panchal, M. S. Abdo and A. M. Saeed. On local problem for fractional integro-differential equation in Banach space. European journal of scientific researche, pages 320–334, 2019.
R. L. Magin. Fractional Calculus in Bioengineering. Begell House Publishers, Danbury, CT, USA, 2006.
Z. Odibat. Approximations of fractional integral and Caputo fractional derivatives. Com- puters and Mathematics with Applications, 178:527–533, 2006.
Z. Odibat. Analytic study on linear systems of fractional differential equations. Computers and Mathematics with Applications, 59:1171–1183, 2010.
I. Podlubny. Fractional differential equations. Mathematics in Science and Engineering, 198:Acad. Press, San–Diego, 1999.
S. Sivasundaram, S. Abbas and M. Benchohra. Ulam stability for partial fractional differ- ential inclusions with multiple delay and impulses via Picard operators. Nonlinear Stud., 20(4):623–641, 2013.
A. Jameel, S. Momani and S. Al-Azawi. Local and global uniqueness theorems on fractional integro-differential equations via Bihari’s and Gronwall’s inequalities. Soochow Journal of Mathematics, 33:619, 2007.
J. Wu and Y. Liu. Existence and uniqueness of solutions for the fractional integro-differential equations in Banach spaces. Electronic J Diff. Equ., 2009:1–8, 2009.
Y. Zhou. Basic theory of fractional differential equations. 6. World Scientific, Singapore, 2004.
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