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Abstract We prove the Hyers-Ulam-Rassias stability of homomorphisms in real Banach algebras and of generalized derivations on real Banach algebras for the following Cauchy-Jensen functional equations: "Equation missing", "Equation missing", which were introduced and investigated by Baak (2006). The concept of Hyers-Ulam-Rassias stability originated from Th. M. Rassias' stability theorem that appeared in his paper (1978).

The current study reveals the impact of MHD heat transfer properties of an incompressible viscous fluid were numerically solved across a continuously expanding horizontal cylinder immersed in a porous material in the existence of internal heat production/sink. The partial differential equations which govern the fluid flow with boundary constraints were converted to a collection of non-linear ODE’s with the aid of similarity variables and then numerically solved by using Keller-Box approach. The

We prove the generalized Hyers‐Ulam stability of the following functional inequalities: , , in the spirit of the Rassias stability approach for approximately homomorphisms.

Blockchain technology must have sparked widespread interest, applications associated with data monitoring, banking sectors, computer security, the Internet of Things, and food chemistry to the healthcare sector and cognitive science. The use of multimedia in the healthcare architecture also allows for the storage, processing and transmission of patient information in a wide range of formats such as images, text and audio over the Internet using various smart particles. However, managing large am

The topic of fluid flow through disks is important due to a broad range of its applications in industries, engineering, and scientific fields. The objective of the current article is to analyze the bioconvective micropolar nanofluid flow between the coaxial, parallel, and radially stretching double disks in the occurrence of gyrotactic motile microorganisms with convective thermal boundary conditions. Darcy–Forchheimer medium is considered between the double disks that allow the flow horizontall

In this work, N-soliton waves, fusion solutions, mutiple M-lump solutions and the collision phenomena between one-M-lump and one-, two-soliton solutions to the (2 + 1)-dimensional Date-Jimbo-Kashiwara-Miwa equation are successfully revealed. A class of one-, two-, three-soliton, one-, two-fusion solutions are derived via the Hirota bilinear method and 1-M-lump, 2-M-lump solutions are constructed via the long-wave method. Moreover, physical collision phenomenon of 1-M-lump with one-, two-soliton

Using the fixed point method, we prove the generalized Hyers-Ulam stability of the quadratic functional equation f(2x+y)=4f(x)+f(y)+f(x+y)−f(x−y) in Banach spaces.

Abstract This paper aims to investigate the class of fifth-order Korteweg–de Vries equations by devising suitable novel hyperbolic and exponential ansatze. The class under consideration is endowed with a time-fractional order derivative defined in the conformable fractional derivative sense. We realize various solitons and solutions of these equations. The fractional behavior of the solutions is studied comprehensively by using 2D and 3D graphs. The results demonstrate that the methods mentioned

In this paper, a nonlinear fractional emerging telecommunication model with higher–order dispersive cubic–quintic is studied by using two recent computational schemes. This kind of model is arising in many applications such as machine learning and deep learning, cloud computing, data science, dense sensor network, artificial intelligence convergence, integration of Internet of Things, self–service IT for business users, self-powered data centers, and dense sensor networks (DSNs) that is used in

New dual-wave soliton solutions are addressed for the two-mode Sawada-Kotera (TmSK) equation arising in fluids by the modified Kudryashov and new auxiliary equation methods. As outcomes, bright, dark, periodic, and singular-periodic dual-wave solutions are obtained. The graphs of the solutions are provided to show the impact of the parameters. A comparison between our solutions and the existing ones is carried out.

Abstract This research is conducted to investigate heat and mass transport past over a stretched surface having pores in a pseudo-plastic model. To study porosity effect, Darcy Forchheimer relation is used. Thermal and mass transport expressions are derived by engaging the double diffusion theories as extensively used by researchers proposed by Cattaneo and Christov. Furthermore, the thermal performance is studied by mixing the tri-hybrid nanoparticles in a pseudo-plastic material. The phenomeno

Abstract This paper studies the analytical, semi-analytical, and numerical solutions of the Cahn–Allen equation, which plays a vital role in describing the structure of the dynamics for phase separation in Fe – Cr – X ( $X=Mo,Cu$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>X</mml:mi><mml:mo>=</mml:mo><mml:mi>M</mml:mi><mml:mi>o</mml:mi><mml:mo>,</mml:mo><mml:mi>C</mml:mi><mml:mi>u</mml:mi></mml:math> ) ternary alloys. The modified Khater method, the Adomian decomposition met