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In this manuscript, we derive and examine the analytical solution for the solid tumor invasion model of fractional order. The main aim of this work is to formulate a solid tumor invasion model using the Caputo fractional operator. Here, the model involves a system of four equations, which are solved using an approximate analytical method. We used the fixed-point theorem to describe the uniqueness and existence of the model's system of solutions and graphs to explain the results we achieved using this approach. The technique used in this manuscript is more efficient for studying the behavior of this model, and the results are accurate and converge swiftly. The current study reveals that the investigated model is time-dependent, which can be explored using the fractional-order calculus concept. [ABSTRACT FROM AUTHOR]

In this paper, we solved a model of a well-known infectious disease called dengue fever via fractional natural decomposition and modified Predictor–Corrector (PC) methods. A study of the dengue epidemic in the Cape Verde Islands off the coast of West Africa in 2009 has been resumed here for a better understanding of the results. The results are obtained using Liouville–Caputo and new generalized Caputo-type fractional derivatives. The numerical simulations are presented for various orders of given derivatives. Existence and uniqueness analysis of the given problem are also performed in the new generalized Caputo sense. The explored results are verified using figures. The main target of this paper is to explore the different dynamics of the given dengue fever model via two types of fractional numerical algorithms. [ABSTRACT FROM AUTHOR]

The pivotal aim of the present work is to find the solution for fractional Caudrey-Dodd-Gibbon (CDG) equation using q-homotopy analysis transform method (q-HATM). The considered technique is graceful amalgamations of Laplace transform technique with q-homotopy analysis scheme, and fractional derivative defined with Atangana-Baleanu (AB) operator. The fixed point hypothesis considered in order to demonstrate the existence and uniqueness of the obtained solution for the projected fractional-order model. In order to illustrate and validate the efficiency of the future technique, we analysed the projected model in terms of fractional order. Moreover, the physical behaviour of q-HATM solutions have been captured in terms of plots for diverse fractional order and the numerical simulation is also demonstrated. The obtained results elucidate that, the considered algorithm is easy to implement, highly methodical as well as accurate and very effective to examine the nature of nonlinear differential equations of arbitrary order arisen in the connected areas of science and engineering.

The object of this paper is to study (∈)-Lorentzian para-Sasakian manifolds. Some typical identities for the curvature tensor and the Ricci tensor of (∈)-Lorentzian para-Sasakian manifold are investigated. Further, we study globally φ-Ricci symmetric and weakly φ-Ricci symmetric (∈)-Lorentzian para-Sasakian manifolds and obtain interesting results. [ABSTRACT FROM AUTHOR]

In this paper, we study α-cosymplectic manifold M admitting ∗ -Ricci tensor. First, it is shown that a ∗ -Ricci semisymmetric manifold M is ∗ -Ricci flat and a ϕ -conformally flat manifold M is an η -Einstein manifold. Furthermore, the ∗ -Weyl curvature tensor W ∗ on M has been considered. Particularly, we show that a manifold M with vanishing ∗ -Weyl curvature tensor is a weak ϕ -Einstein and a manifold M fulfilling the condition R E 1 , E 2 ⋅ W ∗ = 0 is η -Einstein manifold. Finally, we give a characterization for α-cosymplectic manifold M admitting ∗ -Ricci soliton given as to be nearly quasi-Einstein. Also, some consequences for three-dimensional cosymplectic manifolds admitting ∗ -Ricci soliton and almost ∗ -Ricci soliton are drawn. [ABSTRACT FROM AUTHOR]

In this paper we study NMCP manifolds, which are (2p+2q+2)--dimensional differential manifolds with an normal metric contact pair structure. The aim of the study is to examine the Riemannian geometry of normal metric contact pair manifolds under certain conditions related to the *--Ricci tensor. We prove that a *--Ricci-semi-symmetric NMCP manifold is *--Ricci-flat, and that a *--generalized quasi-Einstein NMCP manifold cannot be *--Ricci-semi-symmetric. Finally, we consider the concircular curvature tensor on NMCP manifolds and prove that a concircular flat NMCP manifold is locally isometric to (2p+2q+2)-dimensional hyperbolic space. [ABSTRACT FROM AUTHOR]

n this paper, we consider invariant submanifolds of an (€)-Sasakian manifolds. We show that if the second fundamental form of an invariant submanifold of a (€)-Sasakian manifold is recurrent then the submanifold is totally geodesic. We also prove that, invariant submanifolds of an Einstein (€)-Sasakian manifolds satisfying the conditions C(X, Y ) · σ = 0 and C(X, Y ) · ∇σ = 0 with €r ≠ n(n − 1) are also totally geodesic. [ABSTRACT FROM AUTHOR]

In this paper, we find the solutions for two-dimensional biological population model having fractional order using fractional natural decomposition method (FNDM). The proposed method is a graceful blend of decomposition scheme with natural transform, and three examples are considered to validate and illustrate its efficiency. The nature of FNDM solution has been captured for distinct arbitrary order. In order to illustrate the proficiency and reliability of the considered scheme, the numerical simulation has been presented. The obtained results illuminate that the considered method is easy to apply and more effective to examine the nature of multi-dimensional differential equations of fractional order arisen in connected areas of science and technology. [ABSTRACT FROM AUTHOR]

The aim of this paper is to study weakly symmetries of Kenmotsu manifolds with respect to quarter-symmetric metric connection. We investigate the properties of weakly symmetric, weakly Ricci-symmetric and weakly concircular Ricci-symmetric Kenmotsu manifolds with respect to quarter symmetric metric connection and obtain interesting results. [ABSTRACT FROM AUTHOR]

In this paper, a systematic study of Kenmotsu pseudo-metric manifolds are introduced. After studying the properties of this manifolds, we provide necessary and sufficient condition for Kenmotsu pseudo-metric manifold to have constant φ-sectional curvature, and prove the structure theorem for ξ-conformally flat and φ-conformally flat Kenmotsu pseudo-metric manifolds. Next, we consider Ricci solitons on this manifolds. In particular, we prove that an η-Einstein Kenmotsu pseudo-metric manifold of dimension higher than 3 admitting a Ricci soliton is Einstein, and a Kenmotsu pseudo-metric 3-manifold admitting a Ricci soliton is of constant curvature ε. [ABSTRACT FROM AUTHOR]