This manuscript is based on the standard fractional calculus iteration procedure conformable derivatives. We introduce new integration and differentiation operators. define spaces present some theorems related to these

Abstract Generalization of fractional differential operators was subjected to an intense debate in the last few years order contribute a deep understanding behavior complex systems with memory effect. In this article, Caputo-type modification Hadamard derivatives is introduced. The properties modified are studied.

In this article, we study generalized fractional derivatives that contain kernels depending on a function the space of absolute continuous functions. We generalize Laplace transform in order to be applicable for integrals and apply solve some ordinary differential equations frame under discussion.

In this manuscript we define the right fractional derivative and its corresponding integral for newly suggested nonlocal with Mittag-Leffler kernel.Then, obtain related integration by parts formula.We use Q-operator to confirm our results.The Euler-Lagrange equations are reported one illustrative example is discussed.

In this manuscript, we define the generalized fractional derivative onWe present some of properties derivatives these functions and then their Caputo version.

In this manuscript we propose the discrete versions for recently introduced fractional derivatives with nonsingular Mittag-Leffler function. The properties of such differences are studied and integration by parts formulas proved. Then a variational problem is considered an illustrative example. Finally, some more tools these their have been obtained.

Abstract This paper is devoted to the study of Caputo modification Hadamard fractional derivatives. From here and after, by Caputo-Hadamard derivative, we refer this modified derivative (Jarad et al. in Adv. Differ. Equ. 2012:142, 2012, p.7). We present generalization fundamental theorem calculus (FTFC) setting. Also, several new related results are presented.

In this article, we introduce a new extension of b-metric spaces, called controlled metric type by employing control function α ( x , y ) the right-hand side b-triangle inequality. Namely, triangle inequality in defined will have form, d ≤ z + for all ∈ X . Examples spaces that are not extended sense Kamran et al. given to show our is different. A Banach contraction principle on and an example illustrate usefulness structure extension.

The present paper aims to define three new notions: Θ e -contraction, a Hardy–Rogers-type and an interpolative -contraction in the framework of extended b-metric space. Further, some fixed point results via these notions study endeavors toward feasible solution would be suggested for nonlinear Volterra–Fredholm integral equations certain types, as well fractional differential equation Caputo type by using obtained results. It also considers numerical example indicate effectiveness this technique.

The thermal management of the flow hybrid nanofluid within conical gap between a cone and disk is analyzed. Four different cases are examined, including (1) stationary rotating (2) (3) in same direction (4) opposite directions. magnetic field strength [Formula: see text] added to modeled problem that applied along z-direction. This work actually explores role heat transfer, which performs plate-cone viscometer. A special type nanoliquid containing copper Cu ferrite Fe3O4 nanoparticles...

In current investigation, a novel implementation of intelligent numerical computing solver based on multi-layer perceptron (MLP) feed-forward back-propagation artificial neural networks (ANN) with the Levenberg-Marquard algorithm is provided to interpret heat generation/absorption and radiation phenomenon in unsteady electrically conducting Williamson liquid flow along porous stretching surface. Heat investigated by taking convective boundary condition both velocity thermal slip phenomena....

Abstract This manuscript is related to establishing appropriate results for the existence and uniqueness of solutions a class nonlinear impulsive implicit fractional-order differential equations (FODEs). It remarkable that have attracted great popularity due various important applications in mathematical modeling real-world phenomena/processes, particularly biological or biomedical engineering domains as well control theory. The mentioned problem considered under four-point nonlocal boundary...

Inventory control is a widely discussed topic in the real world, and recently, it has become closely linked to concerns about carbon emissions global warming. Global warming pressing issue, mainly due lack of awareness action. Traditional inventory models, which typically use integer-order differential equations, overlook memory aspect system. Addressing management essential our efforts combat This paper introduces novel approach by incorporating emission costs within fuzzy environment....

Abstract Heat and mass transfer rate by using nanofluids is a fundamental aspect of numerous industrial processes. Its importance extends to energy efficiency, product quality, safety, environmental responsibility, making it key consideration for industries seeking improve their operations, reduce costs, meet regulatory requirements. So, the principal objective this research analyze heat three-dimensional magneto hydrodynamic nanoliquid movement with thermal radiation chemical reaction over...

Viral infections pose significant threats to public health globally. Understanding the behavior, transmission, and epidemiology of viruses is essential for developing strategies prevent, control, manage outbreaks. Mathematical models help in identifying emerging viral pathogens, assessing their risks, implementing effective measures mitigate impact. In this work, we formulate dynamics Covid-19 infection with effect vaccination fractional framework. Our study mainly concerned dynamical...

Soliton theory research has a substantial impact on the application of nonlinear sciences in different fields. This led to significant increase focus researchers study solitary waves recent years. explores diverse dynamic behaviors exhibited by soliton solutions within framework neuron model. In neuroscience, this model is regarded as an important tool for comprehending initiation and propagation action potentials along axons through thermodynamic nerve pulse transmission. The proposed...