Combination of integral and projected differential transform methods for time-fractional gas dynamics equations

Shah, Kunjan; Singh, Twinkle; Kılıçman, Adem

doi:10.1016/j.asej.2016.09.012

Cited by 22 publications

(10 citation statements)

References 18 publications

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“…The following are some properties of new integral transform Theorem 2.8. ((Kunjan et al, 2017)) aÞ The new integral transform of @ n u @t n is given by…”

Section: New Integral Projected Differential Transform Methods (Nipdtm)mentioning

confidence: 99%

A comparative study of analytical solutions of space-time fractional hyperbolic-like equations with two reliable methods

Singh

Gupta

2019

Arab Journal of Basic and Applied Sciences

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This paper deals with a comparative study of analytical solutions of ðn þ 1Þ-dimensional space-time fractional hyperbolic-like equations (with Caputo type fractional derivatives) using two reliable semi-analytical methods: "new integral projected differential transform method (NIPDTM)" and "fractional reduced differential transform method (FRDTM)". Three test problems are carried out in order to illustrate the efficiency of these methods. The computed results are also compared with the results fromo various schemes, in the literature. The computed series solutions from either method converge to the exact solutions. FRDTM solutions are easy to compute without using any transformation as compared to NIPDTM, but FRDTM needs more iterations to obtain the solutions with the same accuracy.

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“…The following are some properties of new integral transform Theorem 2.8. ((Kunjan et al, 2017)) aÞ The new integral transform of @ n u @t n is given by…”

Section: New Integral Projected Differential Transform Methods (Nipdtm)mentioning

confidence: 99%

A comparative study of analytical solutions of space-time fractional hyperbolic-like equations with two reliable methods

Singh

Gupta

2019

Arab Journal of Basic and Applied Sciences

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“…Let A(x, v) be Kashuri Fundo transform of f (x, t). The Kashuri Fundo transform of Caputo fractional derivative is defined [20]:…”

Section: Kashuri Fundo Transform Of Caputo Fractional Derivativementioning

confidence: 99%

Application of Kashuri Fundo transform and homotopy perturbation methods to fractional heat transfer and porous media equations

Peker

ÇUHA

2022

Therm sci

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Integral transformations have been used for a long time in the solution of differential equations either solely or combined with other methods. These transforms provide a great advantage in reaching solutions in an easy way by transforming many seemingly complex problems into a more understandable format. In this study, we used an integral transform, namely Kashuri Fundo transform, by blending with the homotopy perturbation method for the solution of non-linear fractional porous media equation and time-fractional heat transfer equation with cubic non-linearity.

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“…There are many different studies in the literature that reveal the accuracy of these statements [11][12][13][14][15][16][17][18][19][20][21]. There are many studies that show that it gives effective results when used by blending with different methods to reach solutions of nonlinear and fractional differential equations [22][23][24][25][26][27][28][29][30][31][32]. In this study, we demonstrate that the Kashuri Fundo transform, based on Newton's cooling law, which is modeled with first-order differential equations, is an effective, reliable and time-saving method for reaching solutions of first-order differential equations.…”

Section: Introductionmentioning

confidence: 99%

Analytical Solution of Newton s Law of Cooling Equation via Kashuri Fundo Transform

Peker,

Çuha,

Peker

2024

neufmbd

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Geçmişte olduğu gibi günümüzde de fiziksel olayların anlaşılması, doğru bir şekilde yorumlanabilmesi ve modellenmesi gelişmiş matematiksel yöntemlerin kullanılmasını gerektirir. Bu bağlamda, Newton'un soğuma yasası gibi ısı transferi problemlerinin çözümü, integral dönüşümü gibi güçlü matematiksel araçlarla karmaşık hesaplamalara gerek kalmadan, doğru, güvenilir ve kolaylıkla elde edilir. Newton'un soğuma yasası bir cismin sıcaklığının çevresel sıcaklıkla nasıl etkileşime girdiğini ve zaman içinde nasıl değiştiğini diferensiyel denklem modelleriyle ifade eder. Değişkenler ve değişim hızları arasındaki karmaşık ilişkileri ifade eden bu denklemler, fizikçilerin kesin matematiksel modeller formüle etmelerine olanak tanıyarak, fiziksel sistemlerin davranışlarına ilişkin doğru yorumlar yapılmasını sağlarlar. Diferensiyel denklemlerin çözümlerini elde etmeye yönelik hesaplamalar, cebirsel denklemlere ilişkin hesaplamalardan daha karmaşık olabilir. Bundan dolayı, bu denklemlerin çözümlerini elde etmek için farklı yöntemler kullanılmıştır. Bu makalede, Newton'un soğuma yasasının integral dönüşümlerinin bir çeşidi olan Kashuri Fundo dönüşümü ile çözümünü ve bu yaklaşımın fizik, biyokimya, ekonomi, finans, mühendislik vb. alanlarda yer alan farklı matematiksel modellerin çözümlerine ulaşmada kullanılabilecek etkili ve güvenilir bir yöntem olduğunu ortaya koyuyoruz.

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Combination of integral and projected differential transform methods for time-fractional gas dynamics equations

Cited by 22 publications

References 18 publications

A comparative study of analytical solutions of space-time fractional hyperbolic-like equations with two reliable methods

A comparative study of analytical solutions of space-time fractional hyperbolic-like equations with two reliable methods

Application of Kashuri Fundo transform and homotopy perturbation methods to fractional heat transfer and porous media equations

Analytical Solution of Newton s Law of Cooling Equation via Kashuri Fundo Transform

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