Affiliation:
1. Department of Mathematics , University of Peshawar , Peshawar 25000 , Pakistan
Abstract
Abstract
In this manuscript, we study the existence, uniqueness and various kinds of Ulam stability including Ulam–Hyers stability, generalized Ulam– Hyers stability, Ulam–Hyers–Rassias stability, and generalized Ulam–Hyers– Rassias stability of the solution to an implicit nonlinear fractional differential equations corresponding to an implicit integral boundary condition. We develop conditions for the existence and uniqueness by using the classical fixed point theorems such as Banach contraction principle and Schaefer’s fixed point theorem. For stability, we utilize classical functional analysis. The main results are well illustrated with an example.
Reference41 articles.
1. [1] Abbas, Saïd et al. Implicit Fractional Differential and Integral Equations: Existence and Stability. Vol. 26 of De Gruyter Series in Nonlinear Analysis and Applications. Walter de Gruyter GmbH & Co KG, 2018. Cited on 6.
2. [2] Ahmad, Bashir, Ahmed Alsaedi, and Badra S. Alghamdi. “Analytic approximation of solutions of the forced Duffing equation with integral boundary conditions.” Nonlinear Anal. Real World Appl. 9, no. 4 (2008): 1727-1740. Cited on 6.
3. [3] Ahmad, Bashir and Ahmed Alsaedi. “Existence of approximate solutions of the forced Duffing equation with discontinuous type integral boundary conditions.” Nonlinear Anal. Real World Appl. 10, no. 1 (2009): 358-367. Cited on 6.
4. [4] Ali, Arshad, Faranak Rabiei, and Kamal Shah. “On Ulams type stability for a class of impulsive fractional differential equations with nonlinear integral boundary conditions.” J. Nonlinear Sci. Appl. 10, no. 9 (2017): 4760-4775. Cited on 6.
5. [5] Ali, Zeeshan, Akbar Zada, and Kamal Shah. “Ulam stability results for the solutions of nonlinear implicit fractional order differential equations.” Hacet. J. Math. Stat. 48, no. 4 (2019): 1092-1109. Cited on 7.
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