Using Shehu integral transform to solve fractional order Caputo type initial value problems

• Autorzy: Qureshi Sania , Kumar Prem

Identyfikatory

DOI

10.17512/jamcm.2019.2.07

• Języki publikacji: EN

Abstrakty

EN

In the present research analysis, linear fractional order ordinary differential equations with some defined condition (s) have been solved under the Caputo differential operator having order α > 0 via the Shehu integral transform technique. In this regard, we have presented the proof of finding the Shehu transform for a classical nth order integral of a piecewise continuous with an exponential nt h order function which leads towards devising a theorem to yield exact analytical solutions of the problems under investigation. Varying fractional types of problems are solved whose exact solutions can be compared with solutions obtained through existing transformation techniques including Laplace and Natural transforms.

Słowa kluczowe

EN

ordinary differential equations; Laplace transform; Riemann-Liouville integral

PL

równanie różniczkowe zwyczajne; transformata Laplace'a; całka Riemann-Liouville

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2019
• Tom: Vol. 18, nr 2
• Strony: 75--83
• Opis fizyczny: Bibliogr. 25 poz.

Twórcy

autor

Qureshi Sania

• Department of Basic Sciences and Related Studies, Mehran University of Engineering and Technology Jamshoro 76062, Pakistan

autor

Kumar Prem

• Department of Basic Sciences and Related Studies, Mehran University of Engineering and Technology Jamshoro 76062, Pakistan

Bibliografia

• [1] Peng, G. (2007). Synchronization of fractional order chaotic systems. Physics Letters A, 363(5-6), 426-432.
• [2] Atangana, A., & Qureshi, S. (2019). Modeling attractors of chaotic dynamical systems with fractal–fractional operators. Chaos, Solitons & Fractals, 123, 320-337.
• [3] Yusuf, A., Qureshi, S., Inc, M., Aliyu, A.I., Baleanu, D., & Shaikh, A.A. (2018). Two-strain epidemic model involving fractional derivative with Mittag-Leffler kernel. Chaos: An Interdisciplinary Journal of Nonlinear Science, 28(12), 123121.
• [4] Qureshi, S., & Yusuf, A. (2019). Modeling chickenpox disease with fractional derivatives: From Caputo to Atangana-Baleanu. Chaos, Solitons & Fractals, 122, 111-118.
• [5] Ullah, S., Khan, M.A., & Farooq, M. (2018). A fractional model for the dynamics of TB virus. Chaos, Solitons & Fractals, 116, 63-71.
• [6] Qureshi, S., & Yusuf, A. (2019). Fractional derivatives applied to MSEIR problems: Comparative study with real world data. The European Physical Journal Plus, 134(4), 171.
• [7] Qureshi, S., & Atangana, A. (2019). Mathematical analysis of dengue fever outbreak by novel fractional operators with field data. Physica A: Statistical Mechanics and its Applications, 526, 121127.
• [8] Khan, I. (2019). New idea of Atangana and Baleanu fractional derivatives to human blood flow in nanofluids. Chaos: An Interdisciplinary Journal of Nonlinear Science, 29(1), 013121.
• [9] Singh, J. (2019). A new analysis for fractional rumor spreading dynamical model in a social network with Mittag-Leffler law. Chaos: An Interdisciplinary Journal of Nonlinear Science, 29(1), 013137.
• [10] Singh, J., Kumar, D., Hammouch, Z., & Atangana, A. (2018). A fractional epidemiological model for computer viruses pertaining to a new fractional derivative. Applied Mathematics and Computation, 316, 504-515.
• [11] Imran, M.A., Khan, I., Ahmad, M., Shah, N.A., & Nazar, M. (2017). Heat and mass transport of differential type fluid with non-integer order time-fractional Caputo derivatives. Journal of Molecular Liquids, 229, 67-75.
• [12] Qureshi, S., Yusuf, A., Shaikh, A.A., Inc, M., & Baleanu, D. (2019). Fractional modeling of blood ethanol concentration system with real data application. Chaos: An Interdisciplinary Journal of Nonlinear Science, 29(1), 013143.
• [13] Qureshi, S., Rangaig, N.A., & Baleanu, D. (2019). New numerical aspects of Caputo-Fabrizio fractional derivative operator. Mathematics, 7(4), 374.
• [14] Atangana, A., & Koca, I. (2016). Chaos in a simple nonlinear system with Atangana-Baleanu derivatives with fractional order. Chaos, Solitons & Fractals, 89, 447-454.
• [15] Atangana, A. (2018). Non validity of index law in fractional calculus: A fractional differential operator with Markovian and non-Markovian properties. Physica A: Statistical Mechanics and its Applications, 505, 688-706.
• [16] Osman, M.S., Korkmaz, A., Rezazadeh, H., Mirzazadeh, M., Eslami, M., & Zhou, Q. (2018). The unified method for conformable time fractional Schrodinger equation with perturbation terms. Chinese Journal of Physics, 56(5), 2500-2506.
• [17] Atangana, A., & G´omez-Aguilar, J.F. (2018). Numerical approximation of Riemann-Liouville definition of fractional derivative: From Riemann-Liouville to Atangana-Baleanu. Numerical Methods for Partial Differential Equations, 34(5), 1502-1523.
• [18] Rezazadeh, H., Osman, M.S., Eslami, M., Mirzazadeh, M., Zhou, Q., Badri, S.A., & Korkmaz, A. (2019). Hyperbolic rational solutions to a variety of conformable fractional Boussinesq-Like equations. Nonlinear Engineering, 8(1), 224-230.
• [19] Maitama, S., & Zhao, W. (2019). New integral transform: Shehu transform a generalization of Sumudu and Laplace transform for solving differential equations. International Journal of Analysis and Applications, 17(2), 167-190.
• [20] Watugala, G.K. (1998). Sumudu transform-a new integral transform to solve differential equations and control engineering problems. Mathematical Engineering in Industry, 6(4), 319-329.
• [21] Srivastava, H.M., Minjie, L.U.O., & Raina, R.K. (2015). A new integral transform and its applications. Acta Mathematica Scientia, 35(6), 1386-1400.
• [22] Elzaki, T.M. (2011). The new integral transform ‘Elzaki transform’. Global Journal of Pure and Applied Mathematics, 7(1), 57-64.
• [23] Xiao-Jun, Y.A.N.G. (2016). A new integral transform method for solving steady heat-transfer problem. Thermal Science, 20(3), S639-S642.
• [24] Belgacem, F.B.M., & Silambarasan, R. (2012). Theory of natural transform. Journal - MESA, 3(1), 99-124.
• [25] Podlubny, I. (1999). Fractional Differential Equations: An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of Their Solution and Some of Their Applications (Vol. 198). Elsevier.

Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).