Existence of solutions and a numerical scheme for a generalized hybrid class of n-coupled modified ABC-fractional differential equations with an application

Abstract

<abstract><p>In this article, we investigate some necessary and sufficient conditions required for the existence of solutions for mABC-fractional differential equations (mABC-FDEs) with initial conditions; additionally, a numerical scheme based on the the Lagrange's interpolation polynomial is established and applied to a dynamical system for the applications. We also study the uniqueness and Hyers-Ulam stability for the solutions of the presumed mABC-FDEs system. Such a system has not been studied for the mentioned mABC-operator and this work generalizes most of the results studied for the ABC operator. This study will provide a base to a large number of dynamical problems for the existence, uniqueness and numerical simulations. The results are compared with the classical results graphically to check the accuracy and applicability of the scheme.</p></abstract>

Thermal entry problem for a tube with prescribed heat flux condition using viscoplastic fluid: An extended Graetz problem for Casson fluid with axial conduction and viscous dissipation

“…For the solution of the above problem, we split $${\theta }^*( {{r}^*,{x}^*} )$$ as [31, 45]: $$$$\begin{equation}{\theta }^*\ \left( {{r}^*,{x}^*} \right) = \ {\theta }^*_\infty \left( {{r}^*,{x}^*} \right) + {\theta }_e\left( {{r}^*,{x}^*} \right),\end{equation}$$$$…”

“…The widely utilized Homotopy method (OHAM) is applied to obtain the solution, and it is determined that the Casson fluid and normalized slip both increase entropy generation. Some interesting studies related to non-Newtonian fluids [18][19][20][21][22][23], Graetz problem [24][25][26][27][28][29][30][31][32][33][34][35][36][37][38] gliding bacteria [39][40][41][42] and robust numerical approaches [43][44][45] are worthwhile to mention. Motivated by above mention studies, we aim to elaborate on the impact of axial conduction and viscous dissipation on the Graetz problem inside the tube using Casson viscoplastic fluid under imposed heat flux at the wall.…”

Existence and Uniqueness Theorems for a Variable-Order Fractional Differential Equation with Delay

“…The use of perturbation methods substantially facilitates the understanding of system dynamics that are described by various mathematical methods in the area of nonlinear analysis. Even if a differential equation describing a specific dynamical system may occasionally be difficult to solve or assess, by perturbing the system in some way, we can gain some insight on the system [4][5][6][7].…”

An analysis concerning to the existence of mild solution for Hilfer fractional neutral evolution system on infinite interval

“…For more information, reference the basic books [1–7] and the relevant research articles [8–14]. Very recently, many authors have developed existence results for a coupled system of fractional‐order hybrid boundary value problems with $$$ n $$$ initial and boundary hybrid conditions by using the Hyers–Ulam stability criteria, the measure of noncompactness, degree theory, the Atangana–Baleanu fractional derivative, the $$$ p $$$‐Laplacian operator, and the typhoid model in previous studies [15–18]. Moreover, Khan et al [19] investigated new nonlinear fractional model differential systems by referring to the Caputo–Fabrizio fractional derivative, Volterra integrodifferential equations, Caputo fractional derivative, Mittag–Leffler kernel, singularity, and iterative method.…”