Fractional Differential Equations

In this research, we aim to propose a new fractional model for human liver involving Caputo–Fabrizio derivative with the exponential kernel. Concerning the new model, the existence of a unique solution is explored by using the Picard–Lindelof approach and the fixed-point theory. In addition, the mathematical model is implemented by the homotopy analysis transform method whose convergence is also investigated. Eventually, numerical experiments are carried out to better illustrate the results. Comparative results with the real clinical data indicate the superiority of the new fractional model over the pre-existent integer-order model with ordinary time-derivatives.

A new study on the mathematical modelling of human liver with Caputo–Fabrizio fractional derivative

Combined impact of Cattaneo-Christov double diffusion and radiative heat flux on bio-convective flow of Maxwell liquid configured by a stretched nano-material surface

Integral formulas in Riemannian geometry

2019-nCOV epidemic is one of the greatest threat that the mortality faced since the World War-2 and most decisive global health calamity of the century. In this manuscript, we study the epidemic prophecy for the novel coronavirus (2019-nCOV) epidemic in Wuhan, China by using q-homotopy analysis transform method (q-HATM). We considered the reported case data to parameterise the model and to identify the number of unreported cases. A new analysis with the proposed epidemic 2019-nCOV model for unreported cases is effectuated. For the considered system exemplifying the model of coronavirus, the series solution is established within the frame of the Caputo derivative. The developed results are explained using figures which show the behaviour of the projected model. The results show that the used scheme is highly emphatic and easy to implementation for the system of nonlinear equations. Further, the present study can confirm the applicability and effect of fractional operators to real-world problems.

A new study of unreported cases of 2019-nCOV epidemic outbreaks

New approach for fractional Schrödinger‐Boussinesq equations with Mittag‐Leffler kernel

Analysis of fractional Swift‐Hohenberg equation using a novel computational technique

Correspondence D. G. Prakasha, Department of Mathematics, Faculty of Science, Davangere University, Shivagangothri, Davangere 577002, India. Email: prakashadg@gmail.com In this paper, the q-homotopy analysis transform method (q-HATM) is applied to find the solution for the fractional Lakshmanan-Porsezian-Daniel (LPD) model. The LPD model is the generalization of the non-linear Schrödinger (NLS) equation. The proposed method is graceful fusions of Laplace transform technique with q-homotopy analysis scheme, and the derivative is considered in Caputo sense. In order to validate and illustrate the efficiency of the proposed method, we analysed the projected model in terms of fractional order. Moreover, the physical behaviour of the obtained solution has been captured for the three different cases in terms of 3D and contour plots for diverse values of the fractional order. The obtained results confirm that the future method is easy to implement, highly methodical, and very effective to analyse the behaviour of complex non-linear fractional differential equations exist in the connected areas of science and engineering.

An efficient analytical approach for fractional Lakshmanan‐Porsezian‐Daniel model

Fractional Klein-Gordon-Schrödinger equations with Mittag-Leffler memory

A new solution for fractional extended Fisher–Kolmogorov (FEFK) equation using the q-homotopy analysis transform method (q-HATM) is obtained. The fractional derivative considered in the present work is developed with Atangana–Baleanu (AB) operator, and the technique we consider is a mixture of the q-homotopy analysis scheme and the Laplace transform. The fixed point hypothesis is considered for the existence and uniqueness of the obtained solution of this model. For the validation and effectiveness of the projected scheme, we analyse the FEFK equation in terms of arbitrary order for the two distinct cases. Moreover, numerical simulation is demonstrated, and the nature of the achieved solution in terms of plots for distinct arbitrary order is captured.

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Doddabhadrappla Gowda Prakasha

Papers

New approach for fractional Schrödinger‐Boussinesq equations with Mittag‐Leffler kernel

Analysis of fractional Swift‐Hohenberg equation using a novel computational technique

An efficient analytical approach for fractional Lakshmanan‐Porsezian‐Daniel model

Fractional Klein-Gordon-Schrödinger equations with Mittag-Leffler memory

Analytical approach for fractional extended Fisher–Kolmogorov equation with Mittag-Leffler kernel