Laplace-Carson integral transform for exact solutions of non-integer order initial value problems with Caputo operator

• Autorzy: Kumar Prem , Qureshi Sania

Identyfikatory

DOI

10.17512/jamcm.2020.1.05

• Języki publikacji: EN

Abstrakty

EN

Finding the exact solution to dynamical systems in the field of mathematical modeling is extremely important and to achieve this goal, various integral transforms have been developed. In this research analysis, non-integer order ordinary differential equations are analytically solved via the Laplace-Carson integral transform technique, which is a technique that has not been previously employed to test the non-integer order differential systems. Firstly, it has proved that the Laplace-Carson transform for n-times repeated classical integrals can be computed by dividing the Laplace-Carson transform of the underlying function by n-th power of a real number p which later helped us to present a new result for getting the Laplace-Carson transform for d-derivative of a function under the Caputo operator. Some initial value problems based upon Caputo type fractional operator have been precisely solved using the results obtained thereof.

Słowa kluczowe

EN

ordinary differential equations; Laplace transform; Riemann-Liouville integral

PL

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

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2020
• Tom: Vol. 19, nr 1
• Strony: 57--66
• Opis fizyczny: Bibliogr. 18 poz.

Twórcy

autor

Kumar Prem

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

autor

Qureshi Sania

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

Bibliografia

• [1] Sekerci, Y., & Ozarslan, R. (2020). Oxygen-plankton model under the effect of global warming with nonsingular fractional order. Chaos, Solitons and Fractals, 132, 109532.
• [2] Sekerci, Y., & Ozarslan, R. (2020). Dynamic analysis of time fractional order oxygen in a plankton system. The European Physical Journal Plus, 135(1), 88.
• [3] Sekerci, Y., & Ozarslan, R. (2019). Mathematical modelling of plankton–oxygen dynamics in view of non–singular time fractional derivatives. Physica A: Statistical Mechanics and its Applications, 12391242.
• [4] Abro, K.A. (2020). A fractional and analytic investigation of thermo-diffusion process on free convection flow: an application to surface modification technology. The European Physical Journal Plus, 135(1), 31.
• [5] 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.
• [6] 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.
• [7] 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.
• [8] Atangana, A., & Qureshi, S. (2019). Modeling attractors of chaotic dynamical systems with fractal-fractional operators. Chaos, Solitons & Fractals, 123, 320-337.
• [9] Ghanbari, B., Yusuf, A., & Baleanu, D. (2019). The new exact solitary wave solutions and stability analysis for the (2+ 1) (2+1)-dimensional Zakharov-Kuznetsov equation. Advances in Difference Equations, 2019(1), 1-15.
• [10] Arqub, O.A., & Al-Smadi, M. (2020). An adaptive numerical approach for the solutions of fractional advection–diffusion and dispersion equations in singular case under Riesz’s derivative operator. Physica A: Statistical Mechanics and its Applications, 540, 123257.
• [11] Qureshi, S., & Aziz, S. (2019). Fractional modeling for a chemical kinetic reaction in a batch reactor via nonlocal operator with power law kernel. Physica A: Statistical Mechanics and its Applications, 123494.
• [12] Abu Arqub, O. (2019). Application of residual power series method for the solution of time-fractional Schr¨odinger equations in one-dimensional space. Fundamenta Informaticae, 166(2), 87-110.
• [13] Qureshi, S., & Memon, Z.-U.-N. (2020). Monotonically decreasing behavior of measles epidemic well captured by Atangana–Baleanu–Caputo fractional operator under real measles data of Pakistan. Chaos, Solitons & Fractals, 131, 109478. https://doi.org/10.1016/j.chaos. 2019.109478.
• [14] Atangana, A., & Khan, M.A. (2019). Validity of fractal derivative to capturing chaotic attractors. Chaos, Solitons & Fractals, 126, 50-59.
• [15] Owolabi, K.M., & Atangana, A. (2019). Mathematical analysis and computational experiments for an epidemic system with nonlocal and nonsingular derivative. Chaos, Solitons & Fractals, 126, 41-49.
• [16] Qureshi, S., & Kumar, P. (2019). Using Shehu integral transform to solve fractional order Caputo type initial value problems. Journal of Applied Mathematics and Computational Mechanics, 18(2), 75-83.
• [17] 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.
• [18] 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 ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).