On the analysis of vibration equation involving a fractional derivative with Mittag‐Leffler law

Kumar, Devendra; Singh, Jagdev; Băleanu, Dumitru

doi:10.1002/mma.5903

Cited by 183 publications

(84 citation statements)

References 29 publications

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“…29 Therefore, fractional derivative approaches are suggested in mathematical modeling of biological and physical systems. [30][31][32] In this paper, we developed the fractional-order immune therapy bladder cancer model and used the BCG vaccine for treatment by using the Caputo fractional derivative operator. The fractional-order system is stable in both cases and gives the solution infeasible region for uniqueness, positivity, and boundednes to illustrate the treatment of cancer.…”

Section: Introductionmentioning

confidence: 99%

Analysis and dynamical behavior of fractional‐order cancer model with vaccine strategy

et al. 2020

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In recent year, the world has witnessed the arrival of deadly diseases like cancer over all the global levels. To fight back this disease or control the spread, mankind relies on modeling and medicine to control, cure, and behavior of the cancer diseases. We developed the fractional‐order immunotherapy bladder cancer model and used the BCG vaccine for treatment by using the Caputo fractional derivative operator φɛ(0,1]. A mathematical model has four variables B,E, Ti, Tu which represent the vaccine for the immune system, effector cells, total population of affected, and unaffected cells, respectively. In this model, we have two cases according to the growth rate of cells. The fractional‐order system is stable in both cases and gives the solution infeasible region for uniqueness, positivity, and boundedness to illustrate the treatment of cancer. The effect of fractional parameter on our obtained solutions is presented, and a comparison is made with the classical ordinary derivative operator. It is worthy to observe that fractional derivatives show significant changes and memory effects as compared with ordinary derivatives to control the disease at the initial stage to overcome the risk of living with cancer.

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Section: Introductionmentioning

confidence: 99%

Analysis and dynamical behavior of fractional‐order cancer model with vaccine strategy

et al. 2020

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“…Fractional calculus was an essential element in many recently published articles, such as a fractional biological population model, a fractional SISR-SI malaria disease model, a fractional Biswas-Milovic model, fractional wave equations, fractional reaction-diffusion equations, and nonlinear fractional shock wave equations. More recent published articles related with fractional calculus can be clearly found in [1][2][3][4][5][6][7][8][9]. Fractional differential equations have obtained a remarkable reputation among the mathematicians due to rapid development which is applicable in many fields such as mathematics, chemistry, and electronics.…”

Section: Introductionmentioning

confidence: 99%

Coupled System of Nonlinear Fractional Langevin Equations with Multipoint and Nonlocal Integral Boundary Conditions

Salem

Alzahrani

Alnegga

2020

Mathematical Problems in Engineering

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is research paper is about the existence and uniqueness of the coupled system of nonlinear fractional Langevin equations with multipoint and nonlocal integral boundary conditions. e Caputo fractional derivative is used to formulate the fractional differential equations, and the fractional integrals mentioned in the boundary conditions are due to Atangana-Baleanu and Katugampola. e existence of solution has been proven by two main fixed-point theorems: O'Regan's fixed-point theorem and Krasnoselskii's fixed-point theorem. By applying Banach's fixed-point theorem, we proved the uniqueness result for the concerned problem. is research paper highlights the examples related with theorems that have already been proven. HindawiMathematical Problems in Engineering Volume 2020, Article ID 7345658, 15 pages https://doi.org/10.1155/2020/7345658

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“…The basis of it can be traced back to the letter between L'Hôpital and Leibniz in 1695 (See [1]). In the last three centuries, several mathematicians and physicists have devoted to the developments of the theories of fractional calculus [2][3][4][5][6][7][8][9][10][11][12][13]. Furthermore, fractional and fractal calculus applications are found in various fields [14][15][16][17][18].…”

Section: Introductionmentioning

confidence: 99%

Tempered Fractional Integral Inequalities for Convex Functions

2020

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Certain new inequalities for convex functions by utilizing the tempered fractional integral are established in this paper. We also established some new results by employing the connections between the tempered fractional integral with the (R-L) fractional integral. Several special cases of the main result are also presented. The obtained results are more in a general form as it reduced certain existing results of Dahmani (2012) and Liu et al. (2009) by employing some particular values of the parameters.

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On the analysis of vibration equation involving a fractional derivative with Mittag‐Leffler law

Cited by 183 publications

References 29 publications

Analysis and dynamical behavior of fractional‐order cancer model with vaccine strategy

Analysis and dynamical behavior of fractional‐order cancer model with vaccine strategy

Coupled System of Nonlinear Fractional Langevin Equations with Multipoint and Nonlocal Integral Boundary Conditions

Tempered Fractional Integral Inequalities for Convex Functions

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