Kanika Dhawana, Ramesh Kumar Vatsb,a, Erdal Karapınarc
aYogananda School of AI, Computer and Data Science, Shoolini University, Bajhol, Solan 173229, Himachal Pradesh, India
bDepartment of Mathematics & Scientific Computing, National Institute of Technology, Hamirpur (H.P.)–177005, India
cÇankaya University, Department of Mathematics, Ankara, Turkey
This article focuses on the class of nonlinear implicit Hilfer-type fractional differential equations. By using the non-linear growth condition, we have derived the existence of at least one solution by applying Schauder’s fixed point theorem and using Lipschitz conditions, we have derived the uniqueness of the solution with the help of the Banach contraction principle. In addition, we have discussed the stability analysis by using Ulam–Hyers and Ulam–Hyers–Rassias stabilities. All results of this paper are established in a Banach space instead of ℝ. We illustrate our results with the help of two examples.
Keywords: Fixed point theorems; Hilfer fractional derivative; Implicit differential equations; Ulam’s stability.
Dhawan, K., Vats, R. K., & Karapinar, E. (2023). Qualitative analysis of nonlinear Hilfer fractional implicit differential equations in a Banach space. Advances in the Theory of Nonlinear Analysis and Its Application, 7(5), 141–154.