Nonlinear Functional Analysis and Applications

Kyungnam University, Department of Mathematics Eduaction (경남대학교 수학교육과)
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ON IMPULSIVE SYMMETRIC Ψ-CAPUTO FRACTIONAL VOLTERRA-FREDHOLM INTEGRO-DIFFERENTIAL EQUATIONS

  • Received : 2022.12.30
  • Accepted : 2023.02.24
  • Published : 2023.09.15
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Abstract

We study the appropriate conditions for the findings of uniqueness and existence for a group of boundary value problems for impulsive Ψ-Caputo fractional nonlinear Volterra-Fredholm integro-differential equations (V-FIDEs) with symmetric boundary non-instantaneous conditions in this paper. The findings are based on the fixed point theorem of Krasnoselskii and the Banach contraction principle. Finally, the application is provided to validate our primary findings.

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References

  1. R. Agarwal, S. Hristova and D. O'Regan, Non-instantaneous impulses in Caputo fractional differential equations, Fract. Calc. Appl. Anal., 20 (2017), 595-622.  https://doi.org/10.1515/fca-2017-0032
  2. M. Alesemi, N. Iqbal and A.A. Hamoud, The analysis of fractional-order proportional delay physical models via a novel transform, Complexity, 2022 (2022), 1-13.  https://doi.org/10.1155/2022/2431533
  3. M.R. Ali, A.R. Hadhoud and H.M. Srivastava, Solution of fractional Volterra-Fredholm integrodifferential equations under mixed boundary conditions by using the HOBW method, Adv. Differ. Equ., 2019 (2019), 115. 
  4. A. Anguraj, P. Karthikeyan, M. Rivero and J.J. Trujillo, On new existence results for fractional integrodifferential equations with impulsive and integral conditions, Comput. Math. Appl., 66 (2014), 2587-2594.  https://doi.org/10.1016/j.camwa.2013.01.034
  5. R. Arul, P. Karthikeyan, K. Karthikeyan, P. Geetha, Y. Alruwaily, L. Almaghamsi and E. El-hady, On nonlinear ψ-Caputo fractional integro differential equations involving non-instantaneous conditions, Symmetry, 15 (2023), 1-11. 
  6. S. Asawasamrit, Y. Thadang, S.K. Ntouyas and J. Tariboon, Non-instantaneous impulsive boundary value problems containing Caputo fractional derivative of a function with respect to another function and Riemann-Stieltjes fractional integral boundary conditions, Axioms, 10 (2021), 130. 
  7. D.B. Dhaigude, V.S. Gore and P.D. Kundgar, Existence and uniqueness of solution of nonlinear boundary value problems for ψ-Caputo fractional differential equations, Malaya J. Math., 1 (2021), 112-117.  https://doi.org/10.26637/MJM0901/0019
  8. A. Hamoud, Existence and uniqueness of solutions for fractional neutral Volterra-Fredholm integro differential equations, Adv. Theory Nonlinear Anal. Appl., 4(4) (2020), 321-331.  https://doi.org/10.31197/atnaa.799854
  9. A. Hamoud, M.SH. Bani Issa and K. Ghadle, Existence and uniqueness results for nonlinear Volterra-Fredholm integro-differential equations, Nonlinear Funct. Anal. Appl., 23(4) (2018), 797-805.  https://doi.org/10.7862/rf.2018.9
  10. A. Hamoud and K. Ghadle, Some new uniqueness results of solutions for fractional Volterra-Fredholm integro-differential equations, Iranian J. Math. Sci. Infor., 17(1) (2022), 135-144.  https://doi.org/10.52547/ijmsi.17.1.135
  11. A. Hamoud and N. Mohammed, Existence and uniqueness of solutions for the neutral fractional integro differential equations, Dyna. Conti. Disc. Impulsive Syst. Series B: Appl. Algo., 29 (2022), 49-61. 
  12. A. Hamoud and N. Mohammed, Hyers-Ulam and Hyers-Ulam-Rassias stability of nonlinear Volterra-Fredholm integral equations, Discontinuity, Nonlinearity and Complexity, 11(3) (2022), 515-521.  https://doi.org/10.5890/DNC.2022.09.012
  13. A.A. Hamoud, N.M. Mohammed and R. Shah, Theoretical analysis for a system of nonlinear φ-Hilfer fractional Volterra-Fredholm integro-differential equations, J. Sib. Fed. Univ. Math. Phys., 16(2) (2023), 216-229. 
  14. R. Hilfer, Applications of fractional calculus in physics, Singapore: World Scientific, 2000. 
  15. K. Hussain, A. Hamoud and N. Mohammed, Some new uniqueness results for fractional integro-differential equations, Nonlinear Funct. Anal. Appl., 24(4) (2019), 827-836. 
  16. A. Imran, N. Munawar, T. Muhammad, A.A. Hamoud, H. Emadifar, F. Hamasalh, H. Azizi and M. Khademi, Traveling wave solutions to the Boussinesq equation via Sardar sub-equation technique, AIMS Mathematics, 7(6) (2022), 11134-11149.  https://doi.org/10.3934/math.2022623
  17. K. Ivaz, I. Alasadi and A. Hamoud, On the Hilfer fractional Volterra-Fredholm integro differential equations, IAENG Int. J. Appl. Math., 52(2) (2022), 426-431. 
  18. S. Kailasavalli, M. MallikaArjunan and P. Karthikeyan, Existence of solutions for fractional boundary value problems involving integro-differential equations in Banach spaces, Nonlinear Stud., 22 (2015), 341-358. 
  19. P. Karthikeyan, K. Venkatachalam and S. Abbas, Existence results for fractional impulsive integro differential equations with integral conditions of Katugampola type, Acta Math. Univ. Comenianae, 90 (2021), 421-436. 
  20. A.A. Kilbas, H.M. Srivastava and J.J. Trujillo, Theory and applications of fractional differential equations, Amsterdam: Elsevier, 2006. 
  21. C. Long, J. Xie, G. Chen and D. Luo, Integral boundary value problem for fractional order differential equations with non-instantaneous impulses, Int. J. Math. Anal. Ruse, 14 (2020), 251-266.  https://doi.org/10.12988/ijma.2020.912110
  22. C. Nuchpong, S.K. Ntouyas and J. Tariboon, Boundary value problems of Hilfer-type fractional integro-differential equations and inclusions with nonlocal integro-multipoint boundary conditions, Open Math., 18 (2020), 1879-1894.  https://doi.org/10.1515/math-2020-0122
  23. I. Podlubny, Fractional differential equations, Mathematics in Science and Engineering. Academic Press, New York/London/Toronto 1999. 
  24. A. Salim, M. Benchohra, J.R. Graef and J.E. Lazreg, Boundary value problem for fractional order generalized Hilfer-type fractional derivative with non-instantaneous impulses, Fractal Fract., 5 (2021), 1-21.  https://doi.org/10.3390/fractalfract5010001
  25. J.V.D.C. Sousa and E.C. de Oliveira, A Gronwall inequality and the Cauchy-type problem by means of Ψ-Hilfer operator, Differ. Equ. Appl., 1 (2017), 87-106. 
  26. H.M. Srivastava, Fractional-order derivatives and integrals: Introductory overview and recent developments, Kyungpook Math. J., 60 (2020), 73-116. 
  27. H.M. Srivastava, Some parametric and argument variations of the operators of fractional calculus and related special functions and integral transformations, J. Nonlinear Convex Anal., 22 (2021), 1501-1520. 
  28. D. Yang and J.R. Wang, Integral boundary value problems for nonlinear non-instantaneous impulsive differential equations, J. Appl. Math. Comput., 55 (2017), 59-78.  https://doi.org/10.1007/s12190-016-1025-8
  29. A. Zada, S. Ali and Y. Li, Ulam-type stability for a class of implicit fractional differential equations with non-instantaneous integral impulses and boundary condition, Adv. Differ. Equ., 2017 (2017), 317. 
  30. B. Zhu, B. Han, L. Liu and W. Yu, On the fractional partial integro-differential equations of mixed type with non-instantaneous impulses, Bound. Value Prob., 31(1) (2020), 1-12. https://doi.org/10.1186/s13661-020-01451-z