A note on optimal homotopy asymptotic method for the solutions of fractional order heat- and wave-like partial differential equations

Sarwar, Shahzad; Alkhalaf, Salem; Iqbal, S.; Zahid, Manzoor Ahmad

doi:10.1016/j.camwa.2015.06.017

Cited by 60 publications

(43 citation statements)

References 28 publications

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“…According to the {OHAM} algorithm [36,37], we shall extend this scheme for time fractional Fokker-Planck partial differential equations {tFFPPDEs} in the following steps.…”

Section: Oham Scheme For Time Fractional Parabolic Partial Differentimentioning

confidence: 99%

“…The benefit of OHAM is that it establishs its convergence criteria similar to HAM but more pliable. In various research papers S. Iqbal et al [34][35][36], Sarwar et al [37,38] and Alkhalaf [39] have proved sufficient generalization and trust of this method, achieved well approximate solutions, and presented important applications in science and engineering. The concept of OHAM has been articulated in this paper.…”

Section: Introductionmentioning

confidence: 99%

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Dynamical Study of Fokker-Planck Equations by Using Optimal Homotopy Asymptotic Method

et al. 2019

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In this article, Optimal Homotopy Asymptotic Method (OHAM) is used to approximate results of time-fractional order Fokker-Planck equations. In this work, 3rd order results obtained through OHAM are compared with the exact solutions. It was observed that results from OHAM have better convergence rate for time-fractional order Fokker-Planck equations. The solutions are plotted and the relative errors are tabulated.

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“…According to the {OHAM} algorithm [36,37], we shall extend this scheme for time fractional Fokker-Planck partial differential equations {tFFPPDEs} in the following steps.…”

Section: Oham Scheme For Time Fractional Parabolic Partial Differentimentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Dynamical Study of Fokker-Planck Equations by Using Optimal Homotopy Asymptotic Method

et al. 2019

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“…Example Let us assume that the one‐dimensional time fractional HWPM is written as follows:

^{Y A C} D_{t}^{μ} normalΥ false(η, t false) = \frac{1}{2} η^{2} D_{η η} normalΥ false(η, t false), 0 < μ \leq 1,

where the fractional operator

^{Y A C} D_{t}^{μ}

is taken in new YAC sense with boundary conditions

normalΥ false(0, t false) = 0, normalΥ false(1, t false) = e^{t}

and initial condition (IC)

normalΥ false(η, 0 false) = η^{2}

.…”

Section: Solutions Of Time‐fractional Multidimensional Heat Equationsmentioning

confidence: 99%

“…In an accurate, effective, and powerful technique, namely, fractional‐order reduced differential transform method, has been used to solve HWPMs of arbitrary order. In optimal homotopy asymptotic method is obtained to procure the optimal solutions of HWPMs of arbitrary order. In this work, Edeki et al have been implemented a handy approximation technique, namely, modified differential transform method, for the solutions of HWPMs of arbitrary order in 2016.…”

Section: Introductionmentioning

confidence: 99%

“…The major desire of present effort is to represent some new and interesting properties of new YAC fractional operator, and another purpose is to extend the HPM to solve the time fractional multidimensional heat equations where fractional operator is considered in new YAC sense . Let us consider the multidimensional heat equations with variable coefficient form, which is written as

^{Y A C} D_{t}^{μ} normalΥ false(η, t false) = f_{1} false(η, ξ, ω false) {normalΥ}_{η η} + f_{2} false(η, ξ, ω false) {normalΥ}_{ξ ξ} + f_{3} false(η, ξ, ω false) {normalΥ}_{ω ω},

where

0 < η < a, 0 < ξ < b, 0 < ω < c

. Subject to the Neumann boundary conditions

\begin{matrix} {normalΥ}_{η} false(0, ξ, ω, t false) & = g_{1} false(ξ, ω, t false), {normalΥ}_{η} false(a, ξ, ω, t false) = g_{2} false(ξ, ω, t false), \\ {normalΥ}_{ξ} false(η, 0, ω, t false) & = h_{1} false(η, ω, t false), {normalΥ}_{ξ} false(η, b, ω, t false) = h_{2} false(η, ω, t false), \\ {normalΥ}_{ω} false(η, ξ, 0, t false) & = <...> \end{matrix}

…”

Section: Introductionmentioning

confidence: 99%

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An analysis for heat equations arises in diffusion process using new Yang‐Abdel‐Aty‐Cattani fractional operator

Kumar

Ghosh

Samet

et al. 2020

Math Methods in App Sciences

179

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The heat equation is parabolic partial differential equation and occurs in the characterization of diffusion progress. In the present work, a new fractional operator based on the Rabotnov fractional-exponential kernel is considered. Next, we conferred some fascinating and original properties of nominated new fractional derivative with some integral transform operators where all results are significant. The fundamental target of the proposed work is to solve the multi dimensional heat equations of arbitrary order by using analytical approach homotopy perturbation transform method and residual power series method, where new fractional operator has been taken in new Yang-Abdel-Aty-Cattani (YAC) sense. The obtained results indicate that solution converges to the original solution in language of generalized Mittag-Leffler function. Three numerical examples are discussed to draw an effective attention to reveal the proficiency and adaptability of the recommended methods on new YAC operator. KEYWORDS HPTM and RPSM, multidimensional heat equations, new fractional derivative, new YAC operator, Prabhakar or generalized Mittag-Leffler function MSC CLASSIFICATION 26A33; 34A08; 34A34; 60G22 Math Meth Appl Sci. 2020;43:6062-6080. wileyonlinelibrary.com/journal/mma

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Magnetic micro‐fluidics in 3D microchannel at the micro‐scale: Unlocking nano‐porous electrode potential for lithium‐ion micro‐batteries

Ashraf,

Manzoor,

Iqbal

et al. 2024

Energy Storage

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Enhancing the nanosized‐electrolyte's characteristics in Lithium‐driven micro‐batteries (LIMBs) is indispensable to improve the overall efficiency, security, and lifespan of these energy devices, designing nano‐sized electrolyte with a wide electrochemical stability window while keeping them compatible with electrode materials is one of the improvement goals. Battery technologies must go through this optimization process in order to be used practically. A sensing mechanism to keep an eye on the health of Li‐ion energy devices through the magnetization. Magnetic micro‐fluidic patterns that change could be a sign of battery deterioration or other problems with performance. Li‐ion battery health is one application of magnetic sensing that you can do with magnetic sensing. Battery health variations and other performance problems can be found using magnetic mass transport patterns. Present study examines the effects of magnetic field on Eyring–Powel mass transport in nano‐porous channels over a stretching sheet. The principal equations exhibiting the phenomenon are transformed into non‐linear differential equation by second‐order approximation by using a similarity transformation. Furthermore, a semi‐analytic technique named optimal homotopy asymptotic method (OHAM) is used to solve the transformed Eyring–Powell model. The numerical results demonstrated the impact of variations in velocity, skin‐friction coefficient and Sherwood number for the proposed scheme.

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A note on optimal homotopy asymptotic method for the solutions of fractional order heat- and wave-like partial differential equations

Cited by 60 publications

References 28 publications

Dynamical Study of Fokker-Planck Equations by Using Optimal Homotopy Asymptotic Method

Dynamical Study of Fokker-Planck Equations by Using Optimal Homotopy Asymptotic Method

An analysis for heat equations arises in diffusion process using new Yang‐Abdel‐Aty‐Cattani fractional operator

Magnetic micro‐fluidics in 3D microchannel at the micro‐scale: Unlocking nano‐porous electrode potential for lithium‐ion micro‐batteries

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