The current investigations present the numerical solutions of novel singular nonlinear fifth-order (SNFO) system multi-pantograph differential model (SMPDM), i.e., SNFO–SMPDM. SNFO–SMPDM is obtained using sense second kind typical Emden–Fowler and prediction models. features shape factor, pantograph along with points are provided for all four classes extensive use models observed in engineering mathematical systems, e.g., inverse systems viscoelasticity or creep systems. For correctness...

The spectral collocation method based on the Vieta-Lucas polynomials is introduced here for flow of non-Newtonian Powell-Eyring fluid. attentiveness focused some physical characteristics that emerge numerical simulation flows with thermal radiation, magnetic field, and slip velocity phenomenon. In addition, most significant-physical assumptions to handle in this study are presence stratification phenomenon handling heat generation term energy equation. implemented present an approximate...

This paper describes a new study that looks at how magnetohydrodynamic (MHD) nanofluid moves and transfers heat over porous medium with stretched sheet in straight line. investigates the effects of radiation, viscous dissipation, convective boundary conditions (CBCs) on dynamics nanofluids, an area has received insuffi-cient exploration despite its significance both commercial scientific contexts. The research formulates fundamental conservation equations for mass, momentum, heat,...

A new approximate formula of the fractional derivatives is derived. The proposed based on generalized Laguerre polynomials. Global approximations to functions defined a semi-infinite interval are constructed. presented in terms Caputo sense. Special attention given study convergence analysis and estimate an error upper bound formula. spectral collocation method for solving Logistic differential equation (FLDE). properties polynomials approximation used reduce FLDE solve system algebraic...

Analysis of a steady flow viscous Casson fluid subject to Ohmic dissipation and an induced magnetic field is the main goal here. Through stretched vertical sheet, managed. The energy equation explained in thermodynamical system along with heating. By making assumption that viscosity thermal conductivity are temperature-dependent as described here, accurate assessment heat transfer rate may be carried out. Our research also addresses effect slip velocity. There many applications for fields...

In this work, an approximate analytical solution for the problem of non-Newtonian Casson fluid flow past a porous exponentially stretching sheet with Joule heating and convective boundary condition is obtained using relatively new technique; He’s homotopy perturbation (HPM). The major feature HPM that it does not need small parameters in equations, hence determination classical can be discarded. Due to complete efficiency HPM, becomes practically well suited use field study. Also, solutions...

<abstract><p>This article proposed a useful simulation to investigate the Liouville-Caputo fractional order pollution model's solution behavior for network of three lakes connected by channels. A supposedly new approximation technique using Appell type Changhee polynomials (ACPs) was used treat periodic and linear input models. This work employs spectral collocation method based on properties ACPs. The given creates system algebraic equations from studied model. We verified...

In this paper, we provide a collocation spectral scheme for systems of nonlinear Caputo–Hadamard differential equations. Since the operators contain logarithmic kernels, their solutions can not be well approximated using usual methods that are classical polynomial-based schemes. Hence, construct non-polynomial scheme, describe its effective implementation, and derive convergence analysis in both L2 L∞. addition, numerical results to support our theoretical analysis.

This paper secures soliton solutions to optical couplers in presence of Hamiltonian perturbation terms by the aid undetermined coefficients.Both twin core and multiple are studied.Bright, dark singular obtained for model.The existence criteria solitons also presented.The study is focused Kerr power laws nonlinearity.

The present study’s main focus is regarding the physical properties of a two-dimensional (2D) magneto-hydrodynamic boundary layer non-Newtonian Casson fluid flow that moves due to an exponentially expanding surface with mixed convection heat transfer mechanism. In hydrodynamic and transmission process, combined impact thermal radiation magnetic field influence explored. internal generation owing motion or very viscosity not taken into account. Chebyshev spectral method (CSM) employed in this...

This article deals with a simultaneous reconstruction of unknown initial conditions and space-dependent source function in multi-order time-fractional diffusion problems. We discuss the existence uniqueness direct problem. The problem is presented as regularized optimization converted into variational minimizer for demonstrated. For numerical part, modified Levenberg-Marquardt regularization approach constructed to identify condition function. Several examples one two dimensions are employed...