Results 91 to 100 of about 2,495 (216)

Quartic Functional Equation: Ulam-Type Stability in β,p-Banach Space and Non-Archimedean β-Normed Space

Journal of Mathematics, 2022
In this study, we use the alternative fixed-point approach and the direct method to examine the generalized Hyers–Ulam stability of the quartic functional equation  gu+mv+gu−mv=2m−17m−9gu+2m2−1m2gv−m−12g2u+m2gu+v+gu−v, with a fixed positive integer m/ge2
Ravinder Kumar Sharma, Sumit Chandok
doaj   +1 more source

Hyers-Ulam stability of a generalized Hosszú functional equation

Glasnik matematički, 2002
Let \(Y\) be a Banach space and \(f,g,h,k:{\mathbb R}\to Y\). The Hyers-Ulam stability of the functional equation \(f(x+y-\alpha xy)+g(xy)=h(x)+k(y)\), where \(\alpha\) is a priori chosen parameter, is established (note that for \(f=g=h=k\) and \(\alpha=1\) we obtain Hosszú's equation). In the proof the classical Hyers result on the stability of Cauchy
Jung, Soon-Mo, Sahoo, Prasanna K.
openaire   +3 more sources

An Analysis of Controllability Criteria for Higher‐Order Caputo Fractional Differential Systems With State and Control Delays

International Journal of Differential Equations, Volume 2025, Issue 1, 2025.
The present study investigates the controllability problems for higher‐order semilinear fractional differential systems (HOSLFDSs) with state and control delays in the context of the Caputo fractional derivative. Exploiting the invertibility of the Gramian matrix of fractional order, the necessary and sufficient conditions for the controllability ...
Anjapuli Panneer Selvam, Venkatesan Govindaraj, Raaid Alubady, Sina Etemad, Deepali   +4 more
wiley   +1 more source

Existence and stability of mixed type Hilfer fractional differential equations with impulses and time delay

Results in Applied Mathematics
In this paper, we consider a class of mixed type Hilfer fractional differential equations with noninstantaneous impulses, nonlocal conditions and time delay.
Baoyan Han, Bo Zhu
doaj   +1 more source

Solvability of Implicit Fractional Systems With Nonlocal Conditions in Weighted Functional Spaces

International Journal of Differential Equations, Volume 2025, Issue 1, 2025.
This paper investigates the existence and uniqueness of solutions for a class of nonlinear implicit Riemann–Liouville fractional integro‐differential equations subject to nonlocal conditions in a weighted Banach space. The inclusion of both implicit effects and nonlocal terms introduces additional complexity, making the analysis both challenging and ...
Abdulrahman A. Sharif, Maha M. Hamood, Kirtiwant P. Ghadle, Sining Zheng   +3 more
wiley   +1 more source

A New Approach to the Study of the Existence and Uniqueness of Mild Solutions for an Evolving System by Using Fractional Derivatives in the Deformable Sense

International Journal of Mathematics and Mathematical Sciences, Volume 2025, Issue 1, 2025.
In this work, we study the existence and uniqueness of mild solutions for linear and semilinear control systems using the new deformable fractional derivative. The results have been obtained and presented using the deformable Laplace transform and its inverse, as well as the theory of semigroups and a rigorous application of Banach’s fixed‐point ...
Boulkhairy Sy, Abass Sow, Cheikh Seck, Birendra Nath Mandal   +3 more
wiley   +1 more source

Existence and stability results for a coupled system of Hilfer-Hadamard sequential fractional differential equations with multi-point fractional integral boundary conditions

AIMS Mathematics
In this paper, we study the existence and uniqueness of solutions for a coupled system of Hilfer-Hadamard sequential fractional differential equations with multi-point Riemann-Liouville fractional integral boundary conditions via standard fixed point ...
Ugyen Samdrup Tshering, Ekkarath Thailert, Sotiris K. Ntouyas   +2 more
doaj   +1 more source

On the Stability of the Generalized Psi Functional Equation

Axioms, 2020
In this paper, we investigate the generalized Hyers–Ulam stability for the generalized psi functional equation f ( x + p ) = f ( x ) + φ ( x ) by the direct method in the sense of P. Gǎvruta and the Hyers–Ulam–Rassias stability.
Gwang Hui Kim, Themistocles M. Rassias
doaj   +1 more source

On the generalized Hyers–Ulam stability of module left derivations

Journal of Mathematical Analysis and Applications, 2008
Let \(\mathcal A\) be a unital normed algebra and let \(\mathcal M\) be a unitary Banach left \(\mathcal A\)-module. Assume that \(f:\mathcal{A}\to \mathcal{M}\) is an approximate module left derivation, i.e., it satisfies \[ \| f(x+y)-f(x)-f(y)\| \leq\theta\| x\| ^{p_1}\| y\| ^{p_2} \] and \[ \| f(xy)-x\!\cdot\!f(y)-y\cdot f(x)\| \leq\varepsilon\| x\|
openaire   +2 more sources

Modeling and Analysis of Breast Cancer With Variable‐Order Fractional and Optimal Control Approach

International Journal of Mathematics and Mathematical Sciences, Volume 2025, Issue 1, 2025.
This study presents a novel variable‐order (VO) fractional model (VOFM) to describe breast cancer progression and therapy, incorporating five patient compartments that reflect disease stages and treatment effects, including cardiotoxicity. The model employs the constant proportional Caputo (CPC) VO operator to capture memory effects and time‐varying ...
Yousef S. Almaghrebi, K. R. Raslan, Mohamed A. Abd El Salam, Khalid K. Ali, Muhammad Ahsan   +4 more
wiley   +1 more source