Refined stability of the additive, quartic and sextic functional equations with counter-examples

Article Acoustics

Stability analysis for a tripled system of fractional pantograph differential equations with nonlocal conditions

Hasanen A. Hammad et al.

Summary: The goal of this article is to prove the existence and uniqueness of a tripled fixed point for the fractional pantograph differential equations system. Degree theory with non-local boundary conditions is utilized to derive results supporting the existence of at least one solution. Stability analyses, including Ulam-Hyers and generalized Ulam-Hyers, are also established. An illustrative example is presented to further strengthen the analysis.

JOURNAL OF VIBRATION AND CONTROL (2023)

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Article Mathematics, Applied

Existence and stability results for a coupled system of impulsive fractional differential equations with Hadamard fractional derivatives

Hasanen A. Hammad et al.

Summary: The purpose of this study is to provide findings on the existence, uniqueness, and Hyers-Ulam stability of the solution of an implicit coupled system of impulsive fractional differential equations possessing a fractional derivative of the Hadamard type. The existence and uniqueness results are obtained using a fixed point theorem of the type of Kransnoselskii. Multiple forms of Hyers-Ulam stability are also examined. Finally, an example is provided to support the main results.

AIMS MATHEMATICS (2023)

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Article Mathematics, Applied

Solution and Stability of Quartic Functional Equations in Modular Spaces by Using Fatou Property

N. Uthirasamy et al.

Summary: We propose a novel generalized quartic functional equation and investigate its Hyers-Ulam stability in modular spaces using a fixed point technique and the Fatou property.

JOURNAL OF FUNCTION SPACES (2022)

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Article Multidisciplinary Sciences

Stability and Existence of Solutions for a Tripled Problem of Fractional Hybrid Delay Differential Equations

Hasanen A. Hammad et al.

Summary: The purpose of this paper is to determine the existence of tripled fixed point results for the tripled symmetry system of fractional hybrid delay differential equations. We obtain results which support the existence of at least one solution to our system by applying hybrid fixed point theory. Similar types of stability analysis are presented, and the necessary stipulations for obtaining the solution are established.

SYMMETRY-BASEL (2022)

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Article Multidisciplinary Sciences

Solving a System of Differential Equations with Infinite Delay by Using Tripled Fixed Point Techniques on Graphs

Hasanen A. Hammad et al.

Summary: In this manuscript, similar tripled fixed point results are established under restrictions on a b-metric space endowed with graphs. An example is provided to support the results. These findings extend, generalize, and unify several similar significant contributions in the literature. Additionally, the existence of a solution to a system of ordinary differential equations with infinite delay is derived to further extend the results.

SYMMETRY-BASEL (2022)

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Article Mathematics

Stability of Quartic Functional Equation in Modular Spaces via Hyers and Fixed-Point Methods

Syed Abdul Mohiuddine et al.

Summary: This work introduces a new type of generalized quartic functional equation and obtains the general solution. The stability results for this equation are investigated using the Hyers method and a fixed-point technique, demonstrating the non-stability of a singular case.

MATHEMATICS (2022)

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Article Mathematics, Interdisciplinary Applications

Solving a Fractional-Order Differential Equation Using Rational Symmetric Contraction Mappings

Hasanen A. Hammad et al.

Summary: This manuscript presents new rational symmetric pi-xi-contractions in Ψ-metric spaces and deduces some fixed-points for such contractions. Additionally, related results such as Suzuki-type rational symmetric contractions, orbitally Upsilon-complete, and orbitally continuous mappings in Ψ-metric spaces are introduced. The theoretical results are ultimately shared for studying the existence of solutions to a fractional-order differential equation with one boundary stipulation.

FRACTAL AND FRACTIONAL (2021)

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Article Mathematics