We present a new generalization of the Banach contraction principle in setting Branciari metric spaces.

The Lotka‐Volterra (LV) system is an interesting mathematical model because of its significant and wide applications in biological sciences ecology. A fractional LV the Caputo sense investigated this paper. Namely, we provide a comparative study considered using Haar wavelet Adams‐Bashforth‐Moulton methods. For first method, operational matrix order integration derived used to solve model. main characteristic method convert into algebraic equation which easy solve. To demonstrate efficiency...

We establish fixed point theorems for a new class of contractive mappings. As consequences our main results, we obtain on metric spaces endowed with partial order and cyclic Various examples are presented to illustrate obtained results.

The heat equation is parabolic partial differential and occurs in the characterization of diffusion progress. In present work, a new fractional operator based on Rabotnov fractional‐exponential kernel considered. Next, we conferred some fascinating original properties nominated derivative with integral transform operators where all results are significant. fundamental target proposed work to solve multidimensional equations arbitrary order by using analytical approach homotopy perturbation...

Abstract Epidemiology is the glorious discipline underlying medical research, public health practice, and care evaluation. Nowadays, research on disease models with anonymous parameters a popular issue for researchers working in epidemiology. Due to popularity of this field, new numerical method solution fractional SEIR epidemic measles introduced where derivative taken Caputo sense. We have discussed about framework Genocchi wavelets simulations above model. Furthermore, operational matrix...

This work suggested a new generalized fractional derivative which is producing different kinds of singular and nonsingular derivatives based on types kernels. Two derivatives, namely Yang-Gao-Tenreiro Machado-Baleanu Yang-Abdel-Aty-Cattani the kernels normalized sinc function Rabotnov fractional-exponential are discussed. Further, we presented some interesting properties both proposed with integral transform. The coupling homotopy perturbation Laplace transform method implemented to find...

Abstract The parasitoid is a broad evolutionary association of hymenopteran insects which are well‐known as biological control agents. Parasites different from predators because parasites only take resources one host, whereas eat many preys. preeminent target this study to present fractional model host–parasitoid population dynamical system through the Caputo operator. three dimensional coupled differential equations. This research also investigates possibility for obtaining new chaotic...

We discuss the introduced concept of G-metric spaces and fixed point existing results contractive mappings defined on such spaces. In particular, we show that most obtained theorems can be deduced immediately from metric or quasi-metric MSC:47H10, 11J83.

introduced the notion of Z-contraction, that is, a nonlinear contraction involving new class mappings namely simulation functions.This kind contractions generalizes Banach and unifies several known types contractions.In this paper, we consider pair operators satisfying function in metric space endowed with partial order.For operators, establish coincidence common fixed point results.As applications, related results theory order are deduced.

Abstract We introduce a new concept of generalized metric spaces for which we extend some well-known fixed point results including Banach contraction principle, Ćirić’s theorem, result due to Ran and Reurings, Nieto Rodríguez-López. This recover various topological standard spaces, b -metric dislocated modular spaces.

A new fractional derivative with a non-singular kernel involving exponential and trigonometric functions is proposed in this paper. The suggested operator includes as special case Caputo-Fabrizio derivative. Theoretical numerical studies of differential equations concept are presented. Next, some applications to RC-electrical circuits provided.

Abstract In the present work, a numerical technique for solving general form of nonlinear fractional order integro-differential equations (GNFIDEs) with linear functional arguments using Chebyshev series is presented. The recommended equation its argument produces delay, proportional and advanced non-linear arbitrary Fredholm–Volterra equations. Spectral collocation method extended to study this problem as matrix discretization scheme, where derivatives are characterized in Caputo sense....

Very recently, Yang, Abdel-Aty and Cattani (2019) introduced a new intersting fractional derivative operator with non-singular kernel involving Rabotnov fractional-exponential function. In this paper, we present general framework of the homotopy perturbation transform method (HPTM) for analytic treatment time partial differential equations in sense Yang-Abdel-Aty-Cattani. As applications, wave Yang-Abdel-Aty-Cattani derivatives are solved. The solutions obtained form series Prabhakar functions.

discussion is to expose incorrect property of the generalized metric space introduced by A. Branciari in previous Publ.Math.Debrecen article.