On asymptotic and Hyers-Ulam stability of Hilfer fractional initial value problem involving a $(p_{1} ,p_{2},\dots, p _{n})$-Laplacian operator

[1] R.P. Agarwal and D. O’Regan, Infinite interval problems for differential, difference and integral equations, Kluwer Academic Publisher, Dordrecht, 2001.

[2] S. Ai, Y. Su, Q. Yuan and T. Li, Existence of solutions to fractional differential equations with fractional-order derivative terms, J. Appl. Anal. Comput. 11 (2021), no. 1, 486–520.

[3] A. Zada, J. Alzabut, H. Waheed and I.L. Popa, Ulam–Hyers stability of impulsive integrodifferential equations with Riemann–Liouville boundary conditions, Adv. Difference Equations 2020 (2020), no. 1, 1–50.

[4] A. Zada, S. Ali and Y. Li, Ulam-type stability for a class of implicit fractional differential equations with noninstantaneous integral impulses and boundary condition, Adv. Difference Equations 2017 (2017), no. 1, 1–26.

[5] H. Beddani, M. Beddani and Z. Dahmani, Nonlinear differential problem with p-Laplacian and via Phi-Hilfer approach, solvability and stability analysis, Eur. J. Math. Anal. 1 (2021), 164–181.

[6] N. Benkaci-Ali, Positive solution for the integral and infinite point boundary value Problem for fractional-order differential equation involving a generalized ϕ-Laplacian operator, Abstr. Appl. Anal. 2020 (2020).[

7] N. Benkaci-Ali, Existence of exponentially growing solution and asymptotic stability results for Hilfer fractional (p1,p2,...pn)-Laplacian initial value problem with weighted duffing oscillator, Dyn. Syst. Appl. 30 (2021), no. 12, 1763–1778.

[8] C. Cheng, Z. Feng and Y. Su, Positive solutions of fractional differential equations with derivative terms, Electronic J. Differ. Equ. 215 (2012), 1–27.

[9] C.S. Goodrich, Existence of a positive solution to systems of differential equations of fractional order, Comput. Math. Appl. 62 (2011), no. 3, 1251–1268.

[10] C. Corduneanu, Integral Equations and Stability of Feedback Systems, Academic Press, New York, 1973.

[11] D. Inoan and D. Marian, Semi-Hyers–Ulam–Rassias stability of a Volterra integro-differential equation of order I with a convolution type kernel via Laplace transform, Symmetry 13 (2021), no. 1, 2181.

[12] D. Guo and V. Lakshmikantaham, Nonlinear Problems in Abstract Cones, Academic Press, San Diego, 1988.

[13] A. Granas and J. Dugundji, Fixed Point Theory, Springer-Verlag, New York, 2003.

[14] A. Greenhill, Stability of orbits, Proc. Lond. Math. Soc. 22 (1890/91), 264–305.

[15] H.A. Wahash and S.K. Panchal, Positive solutions for generalized Caputo fractional differential equations using lower and upper solutions method, J. Frac. Calc. Nonlinear Syst. 1 (2020), no. 1, 1–12.

[16] H. Khan, T. Abdeljawad, M. Aslam, R. Ali Khan and A. Khan, Existence of positive solution and Hyers–Ulam stability for a nonlinear singular-delay-fractional differential equation, Adv. Difference Equations 2019 (2019), no. 1, 1–13.

[17] H. Khan, W. Chen, A. Khan, T.S. Khan and Q.M. Al-Madlal, Hyers–Ulam stability and existence criteria for coupled fractional differential equations involving p-Laplacian operator, Adv. Difference Equations 2018 (2018), no. 1, 1–16.

[18] J. Huang, S. M Jung and Y. Li, On Hyers-Ulam stability of nonlinear differential equations, Bull. Korean Math. Soc. 52 (2015), no. 2, 685–697.

[19] J. Valein, On the asymptotic stability of the Korteweg-de Vries equation with time-delayed internal feedback, Math. Control Related Fields 28 (2021).

[20] L. Sun, Hyers-Ulam stability of ϵ-isometries between the positive cones of Lp-spaces, J. Math. Appl. 487 (2020), no. 2, 124014.

[21] M. Ahmad, A. Zada and J. Alzabut, Stability analysis of a nonlinear coupled implicit switched singular fractional differential system with p-Laplacian, Adv. Difference Equations 2019 (2019), no. 1, 1–22.

[22] N. Halidias and I.S. Stamatiou, A note on the asymptotic stability of the semi-discrete method for stochastic differential equations, Monte Carlo Meth. Appl. 28 (2022), no. 1, 13–25.

[23] F.I. Njoku and P. Omari, Stability properties of periodic solutions of a Duffing equation in the presence of lower and upper solutions, Appl. Math. Comput. 135 (2003), 471–490.

[24] R. Ortega, Stability and index of periodic solutions of an equation of Duffing type, Boll. Unione Mat. Ital. 7 (1989), 533–546.

[25] A.G.M. Selvam, D. Baleanu, J. Alzabut, D. Vignesh and S. Abbas, On Hyers–Ulam Mittag-Leffler stability of discrete fractional Duffing equation with application on inverted pendulum, Adv. Difference Equations 2020 (2020), Article Number 456.

[26] F.R. Sharpe, On the stability of the motion of a viscous liquid, Trans. Amer. Math. Soc. 6 (1905), no. 4, 496–503.

[27] S. Omar Shah and A. Zada, Existence, uniqueness and stability of solution to mixed integral dynamic systems with instantaneous and noninstantaneous impulses on time scales, Appl. Math. Comput. 359 (2019), 202–213.

[28] S. Ulam, A Collection of Mathematical Problems, New York, NY, Interscience Publishers, 1960.

[29] J. Vanterler, C. Sousa and E. Capelas de Oliveira, On the Ψ-Hilfer fractional derivative, Commun. Nonlinear Sci. Numer. Simul. 60 (2018), 72–91.