• Nonlinear Functional Analysis and Applications
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• v.29 no.1
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• pp.259-273
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• 2024

In this manuscript, we study the sufficient conditions for existence and uniqueness results of solutions of impulsive Hilfer fractional Volterra-Fredholm integro-differential equations with integral boundary conditions. Fractional calculus and Banach contraction theorem used to prove the uniqueness of results. Moreover, we also establish Hyers-Ulam stability for this problem. An example is also presented at the end.

• Nonlinear Functional Analysis and Applications
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• v.27 no.3
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• pp.513-532
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• 2022

This paper deals with the stability of solutions to 𝜓-Hilfer fractional differential systems. We derive the fundamental solution for the system by using the generalized Laplace transform and the Mittag-Leffler function with two parameters. In addition, we obtained some necessary conditions on the stability of the solutions to linear fractional differential systems for homogeneous, non-homogeneous and non-autonomous cases. Numerical examples are also given to illustrate the behavior of solutions.

• Journal of applied mathematics & informatics
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• v.42 no.2
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• pp.399-415
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• 2024

We looked at nonlocal controllability for Hilfer fractional differential equations with almost sectorial operator in this manuscript. We show certain necessary criteria for nonlocal controllability using the measure of noncompactness and the Mönch fixed point theorem. Finally, we provided theoretical and practical applications are given to demonstrate how the abstract results might be applied.

• Nonlinear Functional Analysis and Applications
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• v.29 no.2
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• pp.501-515
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• 2024

The primary focus of this paper is to thoroughly examine and analyze a coupled system by a Hilfer-Hadamard-type fractional differential equation with coupled boundary conditions. To achieve this, we introduce an operator that possesses fixed points corresponding to the solutions of the problem, effectively transforming the given system into an equivalent fixed-point problem. The necessary conditions for the existence and uniqueness of solutions for the system are established using Banach's fixed point theorem and Schaefer's fixed point theorem. An illustrate example is presented to demonstrate the effectiveness of the developed controllability results.