Rami Ahmad El-Nabulsi

Czech Academy of Science

The fractional calculus of variations is considered today as an important in applied mathematics. It consists of minimizing or maximizing functionals that depend on different types of fractional derivatives and integral operators. This mathematical subject has proved to be relevant because of its motivating implications in describing dissipative an...

In this paper, we propose a nonlocal extension of the mimetic dark matter model based on the FALVA implementation of fractional calculus. Our primary objective to explore how certain properties of dark matter can be modeled within the FALVA framework rather than formulate a phenomenological model. We begin by constructing the action functional of t...

In this paper, we construct a Schwarzschild metric in the fractal dimension based on fractal calculus, and we study the deflection of light near the sun. It was observed that the new fractal spherically symmetric spacetime metric may describe supermassive black holes, which have been detected through various astronomical observations such as SDSS....

In order to alleviate the Hubble tension, we propose a new law for the Hubble parameter that varies periodically with time and we study the validity of the dynamics of a flat Friedmann–Robertson–Walker Universe in the context of a generalized Chern–Simons modified gravity (CSMG). We prove that for specific numerical values of the free parameters in...

In this work, we communicate the issue of Lie algebroids. More precisely, we discuss the subject based on the generalized Stieltjes fractal-like approach of the calculus of variations. We derive the corresponding Euler-Lagrange, geodesics and Wongs equations and we then illustrate, by discussing, the resulting dynamics of a colored particle in the...

Thermodynamical systems having negative heat capacity are characterised by peculiar behaviours, yet they have been reported in several systems ranging from large to nanoscales. We show that negative heat capacity may arise in low-dimensional/nano quantum oscillators due to strong electron correlations observed in underdoped cuprates and quantum wel...

It is well-known that any dynamical system governed by a differential equation containing time derivatives higher than second order unavoidably holds unbounded energy solutions, dubbed ghosts that appear in the Hamiltonian. They correspond to instabilities displayed at the classical level. In this study, we show first that it is possible to constru...

In this study, we introduced a new nonlocal complex derivative operator in fractal dimension based concurrently on the concept of “nonlocal generalized complex backward-forward coordinates” and the “product-like fractal measure”. The quantization of the theory in fractal dimension leads to a higher order Schrödinger equation characterized by a high...

We introduce new types of fractional generalized elliptic operators on a compact Riemannian manifold with Clifford bundle. The theory is applicable in well-defined differential geometry. The Connes-Moscovici theorem gives rise to dimension spectrum in terms of residues of zeta functions, applicable in the presence of multiple poles. We have discuss...

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We study the late-time cosmological dynamics of the Friedmann-Robertson-Walker fractal universe based on power counting renormalizable field in dynamical Chern–Simons modified gravity living in a fractal spacetime. The model is characterized by a time-varying gravitational constant and two-fluids which impose a non-violation of the Bianchi identity...

In this study, novel criteria are derived to ensure the oscillation of solutions in nonlinear advanced noncanonical dynamic equations. The obtained results are reminiscent of the criteria proposed by Hille and Ohriska for canonical dynamic equations. Additionally, this paper addresses a previously unresolved issue found in numerous existing works i...

The von Bertalanffy growth function has been widely used by hydrobiologists to study the lifetime pattern of somatic growth in fishes. Recently, the new ontogenetic growth model has been introduced as a special case of the von Bertalanffy equation based on allometric scaling which has also been of particular importance since it offers the basic too...

CaCO3 coating was applied to the surface of Co0.5Zn0.5Fe2O4 (CZF) nanoparticles by chemical co-precipitation method. CaCO3-coated CZF(CC@CZF) and bare CZF nanoparticles have been characterized by spectroscopy and microscopy techniques. XRD patterns indicate the pure cubic spinel structure of CZF nanoparticles and the growth of CaCO3 layer on the na...

We study the dynamics of particles in cold electron plasma medium based on two dissimilar approaches: the fractional actionlike varia-tional and fractal calculus approaches. In each case, the corresponding Boltzmann and Vlasov-Boltzmann equations were derived. Although the mathematical relationships between fractional calculus and fractal calculus...

An extended non-local field equations characterised by modified dispersion relations have been constructed based on non-local differential and hyperdifferential quantum operators. The dispersion relations obtained are found to be comparable to those obtained within the framework of unified theories and the covariant Kempf–Mangano algebra but free f...

We construct a new cosmological model based on relativistic theory of gravity characterized by massive gravitons. The new Friedmann–Robertson–Walker model is characterized by the presence of a static traversable wormhole, massive gravitons, and a variable gravitational coupling constant. To recover the Bianchi identity, a second cosmic fluid is int...

The phenomenon of solitons characterized by nonlinear structures is widely studied in the literature due to their important implications in various fields of sciences and engineering, mainly space plasma physics. These solitons are described by nonlinear evolution equations, such as the highly nonlinear Korteweg–de Vries (KdV) and Zakharov–Kuznetso...

This paper is concerned with the construction of a phenomenological model for drainage of a liquid in foam in fractal dimensions. Our model is based on the concepts of “product-like fractal measure” introduced to model dynamics in porous media and “complex fractional transform” which converts a fractal space on a small scale to a smooth space with...

We prove the existence of an analogy between spatial long range interactions which are of convolution-type introduced in non-relativistic quantum mechanics and the generalized uncertainty principle predicted from quantum gravity theories. As an illustration, black holes temperatures effects are discussed. It was observed that for specific choices o...

Pennes' bioheat equation is considered one of the most prevalent mathematical equations used to estimate the temperature profile of a tumor in a human body when subjected to thermal ablation and cryoablation. Due to the extensive application of this equation in biomathematics and thermal engineering processes, several models have been proposed in t...

Each spinor has two states and could store a bit of information. Within a biological system, spinors on the heart cells give information bits to spinors on blood cells. Then, these blood cells move and give these information bits to spinors on the neurons of the brain. Spinors within these structures exchange information through photons with the li...

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In this communication, we have constructed a generalized nonlinear Schrödinger equation based on nonlocal quantum momentum square operator. Single and bright singular combo solitons solutions have been obtained from quantum arguments. This study proves that solitons may be used to study nonlinear effects in nonlocal nonlinear media including nonlin...

In this study, we study waves propagation in fractal spaces based on two independent variational approaches: the first one is based on the "product-like fractal measure" introduced by Li and Ostoja-Starzewski in their analysis of nonlinear fractal dynamics in anisotropic porous media whereas the second and another is based on fractal calculus, whic...

The MOSFET is a semiconductor microelectronic single-chip used in different technical aspects in computer engineering and nanotechnology. However, there are many self-assembly micro- and nano-electronic processes generating fractal patterns where millions of metallic nanoparticles are self-assembled into fractal electronic circuits. This proves the...

Bertrand theorem’s states that, among central-force potentials with bound orbits, there are only two types of central-force scalar potentials with the property that all bound orbits are also closed orbits: the inverse-square law and Hooke’s law. These solutions are considered basic examples in classical mechanics since they help in understanding th...

Aluminum doped cobalt ferrite nanoparticles(CoFe2–xAlxO4(x = 0.0 and 0.5)) were synthesized by wet chemical co-precipitation method. X-ray diffraction pattern confirmed the successful doping of the smaller cation of Al³⁺ and the single-phase cubic spinel structure of the prepared nanoparticles. The crystallite size of nanoparticles was examined ~25...

In this communication, three different forms of fractional nonlinear Schrödinger equations have been constructed based on the notion of nonlocal generalized fractional momentum operator, the fractional expansion Riccati method and the notion of Laplacian operator in fractal dimensions. Their physical properties are analyzed and their associated sol...

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Abstract: In this study, we have used the concept of ‘product-like fractal measure’ introduced by Li and Ostoja-Starzewski in their formulation of anisotropic and elastic media to introduce Vlasov equation in fractal dimension. We have been motivated by this new concept since it is safely applied to several systems with length scales bounded by low...

Abstract The objective of this paper is to derive new Hille type and Ohriska type criteria for third-order nonlinear dynamic functional equations in the form of {a2(ζ)φα2([a1(ζ)φα1(xΔ(ζ))]Δ)}Δ+q(ζ)φα(x(g(ζ)))=0, on a time scale T, where Δ is the forward operator on T,α1,α2,α>0, and g,q,ai, i=1,2, are positive rd-continuous functions on T, and φθ(u)...

In this paper, tsunami dynamics and solitary waves are constructed in fractal dimensions based on the concept of product-like fractal measure introduced recently by Li and Ostoja–Starzewski in their formulation of anisotropic continuum media. The tsunami waves are comparable to some extent to varying-speed wave equations which are used in several s...

Casimir effect predicts that two parallel flat neutral plates are attracted to each other due to quantum fluctuations of the electromagnetic field. In this communication, we study Casimir effect based on two different approaches: the first one is correlated to fractional Laplacian by means of fractional derivatives operators whereas the second one...

This paper investigates the bipartite synchronization of memristor-based fractional-order coupled delayed neural networks with structurally balanced and unbalanced concepts. The main result is established for the proposed model using pinning control, fractional-order Jensen’s inequality, and the linear matrix inequality. Further, new sufficient con...

In this work, we develop enhanced Hille-type oscillation conditions for arbitrary-time, second-order quasilinear functional dynamic equations. These findings extend and improve previous research that has been published in the literature. Some examples are given to demonstrate the importance of the obtained results.

In Moffat stochastic gravity arguments, the spacetime geometry is assumed to be a fluctuating background and the gravitational constant is a control parameter due to the presence of a time-dependent Gaussian white noise ξ ( t ) . In such a surrounding, both the singularities of gravitational collapse and the Big Bang have a zero probability of occu...

In this study, the nonlocal fractal neutrons transport equation in fractal dimensions \((\alpha ,\beta )\) is constructed based on the concepts of fractal derivative and a spatially symmetric kernel function which measures the influence of neighbours. The resulting equation is comparable to the Swift–Hohenberg equation which plays a central role in...

The purpose of this paper is to develop, in fractal dimension, the semi-quantitative extension of the Ginzburg-Landau theory of superconductivity. Our theoretical analysis is based on the notion of the non-standard Lagrangian approach which, based on recent studies, offer new insights in the theory of nonlinear differential equations and quantum me...

We discuss spontaneous symmetry breaking in the presence of a new type of symmetric potential based on Fresnel integrals which give an infinite number of minima. Several interesting points were raised, in particular the emergence of massive Goldstone boson and an enhancement of the photon mass. The new theory depends on discrete numbers \(n,N\in {\...

A new higher order Schrödinger equation characterized by a position-dependent mass is introduced based on long-range spatial kernel effects and von Roos arguments. The extended Schrödinger equation depends on the sign of the moments M k , k = 0 , 1 , 2 , … and a stabilized quantum dynamic is realized for M 2 > 0 and M 4 > 0 . We have discussed its...

In this study, the basic concepts of superconductivity based on nonlocal momentum operator have been addressed. The theory is characterized by the presence of higher-order moments and a symmetric kernel which give rise to a higher-derivative superconductivity theory. We have derived the Ginzburg-Landau equations and we have analyzed their propertie...

We study a geometric Ricci flow on a fixed manifold where space and time scales followed the two-scale transform (xβ,tα), α,β>0. The fractal evolution equations are obtained and the resultant Ricci flow is derived accordingly. For slow velocity of the flow, it was observed that Ricci flow is characterized by an anomalous Gaussian measure similar to...

In the current study, Al-substituted cobalt ferrite nanoparticles (NPs), CoFe2–xAlxO4, were synthesized by co-precipitation method. X-ray diffraction patterns for all the prepared ferrite samples confirmed the formation of single-phase cubic spinel structure. The FT-IR spectra show two foremost fundamental absorption bands ranging from about 450 to...

There is great focus on phenomena that depend on their past history or their past state. The mathematical models of these phenomena can be described by differential equations of a self-referred type. This paper is devoted to studying the solvability of a state-dependent integro-differential inclusion. The existence and uniqueness of solutions to a...

Tumors consist of heterogeneous populations of cells. The cell-cell interactions processes play a critical role in cancer invasion and could be influenced by the mutation of cancerous tumor. This study is devoted to the analysis of the temperature distribution of tumor growth based on nonlocal range effects mainly the tumor-tumor influence incorpor...

In this study, a new generalized local fractal derivative operator is introduced and we discuss its implications in classical systems through the Lagrangian and Hamiltonian formalisms. The variational approach has been proved to be practical to describe dissipative dynamical systems. Besides, the Hamiltonian formalism is characterized by the emerge...

Turbulent diffusion flames are considered an active field of research used in many engineering applications of combustion theory. The basic properties of jet diffusion flames were obtained in the literature, and their confrontation with observations and experiments support the mathematical aspects of combustion theory founded by famous researchers...

Despite the recycling challenges in ionic fluids, they have a significant advantage over traditional solvents. Ionic liquids make it easier to separate the end product and recycle old catalysts, particularly when the reaction media is a two-phase system. In the current analysis, the properties of transient, electroviscous, ternary hybrid nanofluid...

The main aim of this paper is to discuss the influence of fractal dimensions on the behavior of the solutions of the Grad-Shafranov equation. Our study is based on the product-like fractal measure approach constructed by Li and Ostoja-Starzewski in their attempt to explore anisotropic fractal continuum media. The fractal Grad-Shafranov equation giv...

In this study, we constructed the seismic wave equation in fractal dimensions based on the concept of product-like fractal measure introduced recently by Li and Ostoja-Starzewski in their formulation of anisotropic media. The solutions of the fractal seismic wave have proved the effect of fractal dimensions on the propagation of this type of wave i...

We study some basic problems arising in ocean–atmosphere dynamics including the ocean surface waves and Rossby waves based on the concept of product-like fractal measure introduced recently by Li and Ostoja-Starzewski in their formulation of anisotropic media. We have derived the fractal fluid equations and we have analyzed several fundamental prob...

The aim of this study is to extend the soliton propagation model in biomembranes and nerves constructed by Heimburg and Jackson for the case of fractal dimensions. Our analyses are based on the product-like fractal measure concept introduced by Li and Ostoja-Starzewski in their attempt to explore anisotropic fractal elastic media and electromagneti...

In this study, we have analyzed the Finsler–Randers manifolds starting from nonstandard Lagrangians formalism which is considered as an emergent phenomenon in the theory of the calculus of variations. These special forms of Lagrangians are motivating since they have explicit dependence on special function. We have proved that their associated usual...

This study treats a new model of nonlocal fractal thermoelasticity beam theory for nanomaterials characterized by an apparent negative thermal conductivity which occurs in shaped graded materials. The model is based on the new concept of "product-like fractal measure" introduced by Li and Ostoja-Starzewski in their formulation of fractal continuum...

In this study, we analyzed the fundamental concepts of solar physics based on the product-like fractal measure concept introduced by Li and Ostoja-Starzewski in their attempt to explore anisotropic fractal elastic media and electromagnetic fields. We constructed the magnetohydrodynamic equations in fractal dimensions. We used these equations to ana...

In classical mechanics, in the case of gravitational and electromagnetic interactions, the force on a particle is usually proportional to its acceleration: The force acts locally on the particle. However, there are situations possible-if the particle moves through a suitable medium, for example, in which the force depends also on the first-time der...

In this study, we proved that damped quadratic nonlinear oscillators similar to Duffing and Helmholtz–Duffing damped equations which emerge in bubble dynamics with time-periodic straining flows and solitary-like wave's dynamics may be derived from a new functional approach based on nonstandard Lagrangians and fractional frictions. The solutions of...

In this article, we construct fluid equations in fractal dimensions based on the concept of the product-like fractal measure introduced by Li and Ostoja-Starzewski in their formulation of anisotropic media. Three main problems were discussed and analyzed: the Rayleigh problem, the steady Burger's vortex and the Kelvin–Helmholtz instability. This st...

In this paper, we study the general solution of the functional equation, which is derived from additive–quartic mappings. In addition, we establish the generalized Hyers–Ulam stability of the additive–quartic functional equation in Banach spaces by using direct and fixed point methods.

In this study, the concept of the product-like fractal measure introduced by Li and Ostoja-Starzewski in their formulation of fractal continuum media is combined with the concept of the fractal time derivative operator. This combination is used to construct a map between the Schrödinger equation which governs the wave function of a quantum–mechanic...

In this study, we have constructed a generalized Schrödinger equation in fractal dimensions characterized by an effective potential which is generated by a position-dependent mass. Our analysis is based on the fractal anisotropy and product-like fractal measure approach introduced by Li and Ostoja-Starzewski in their formulation of continuum media....

In this paper, we investigate the existence results for nonlinear fractional q-difference equations with two different fractional orders supplemented with the Dirichlet boundary conditions. Our main existence results are obtained by applying the contraction mapping principle and Krasnoselskii’s fixed point theorem. An illustrative example is also d...

In this study, a new oscillation criterion for the fourth-order neutral delay differential equation ruxu+puxδu‴α′+quxβϕu=0,u≥u0 is established. By introducing a Riccati substitution, we obtain a new criterion for oscillation without requiring the existence of the unknown function. Furthermore, the new criterion improves and complements the previous...

In this study, the Pennes and Cattaneo–Vernotte bioheat transfer equations in the presence of fractal spatial dimensions are derived based on the product-like fractal geometry. This approach was introduced recently, by Li and Ostoja-Starzewski, in order to explore dynamical properties of anisotropic media. The theory is characterized by a modified...

In this study, we have discussed the implications of acceleration in quantum mechanics by means of a generalized derivative operator (GDO). A new Schrödinger equation is obtained which depends on the reduced Compton wavelength of the particle. We have discussed its implications in quantum mechanics for different types of potentials mainly the infin...

In this study, the Schrödinger equation with position-dependent mass in fractal dimensions is constructed from fractal anisotropy and product-like fractal measure introduced by Li and Ostoja-Starzewski in their formulation of fractal continuum media and elasticity. The theory is characterized by a fractal uncertainty relation and a generalized frac...

This report examines the heat and mass transfer in three-dimensional second grade non-Newtonian fluid in the presence of a variable magnetic field. Heat transfer is presented with the involvement of thermal relaxation time and variable thermal conductivity. The generalized theory for mass flux with variable mass diffusion coefficient is considered...

Fractional theories have gained recently an increasing interest in dynamical systems since they offer some solutions to a number of puzzles in particular nonconservative and dissipative issues. Most of fractional dynamical theories are formulated by means of one occurrence of action that group kinetic energy and potential energy in one single packa...

We study the variational integration problem for Lie algebroids and Finsler manifold in time-dependent fractal dimension. The theory in general is complexified and complex geodesics are obtained accordingly. However, decomplexification or the transition from C→R is possible if the action integral by itself is complexified. Their implications in Fin...

In this study, the fractal neutrons diffusion equation is constructed based on the concept of fractal anisotropy and product-like fractal measure introduced by Li and Ostoja-Starzewski using the method of dimensional regularization. In this approach, the global forms of dynamical equations are cast in forms involving integer-order integrals while t...

A generalized nonlocal uncertainty relation is constructed based on the notion of quantum acceleratum operator obtained in the framework of nonlocal-in-time kinetic energy approach for the case of reversible motion. The new uncertainty relation modified all quantum Hamiltonians and predicts nonlocal corrections to various phenomena at low-dimension...

Graph connectivity theory is important in network implementations, transportation, network routing and network tolerance, among other things. Separation edges and vertices refer to single points of failure in a network, and so they are often sought-after. Chandramouleeswaran et al. introduced the principle of semiring valued graphs, also known as S...

In this study, we discuss string cosmology with solitonic NS–NS matter, which arises when dilaton coupled p-brane gas dominates the universe and is subject to a fractional action motivated from viscosity dissipative effects occurring in the universe. Exact solutions are found from the stationary conditions of the fractional action. It was observed...

The analysis of nuclear reactors in dissimilar geometries is an important topic in sciences and engineering. Two approaches are used in literature for homogeneous systems: computational and analytical methods. In this study, an analytical solution based on a variable coefficient advection is introduced. Such a coefficient is analogous to the additi...

We present a new viable modified theory of gravity in which the matter sector is characterized by a logarithmic Lagrangian density. The modified Einstein’s field equations are derived, and they are characterized by the emergence of an effective gravitational coupling constant and an effective negative cosmological constant both coupled to the Lagra...

In this article, we prove some new oscillation theorems for fourth-order differential equations. New oscillation results are established that complement related contributions to the subject. We use the Riccati technique and the integral averaging technique to prove our results. As proof of the effectiveness of the new criteria, we offer more than o...

In this work, we obtained new sufficient and necessary conditions for the oscillation of second-order differential equations with mixed and multiple delays under a canonical operator. Our methods could be applicable to find the sufficient and necessary conditions for any neutral differential equations. Furthermore, we proved the validity of the obt...

In this study, we have used the concept of product-like fractal measure to analyze the fractal heat transfer in anisotropic media. This concept was introduced by Li and Ostoja-Starzewski in order to study anisotropic fractal elastic and continuum media. The theory is characterized by extended fluid, mass and heat transfer fractal equations besides...

A quantum theory of the mesoscopic LC-circuit based on the product-like fractal measure which was introduced by Li and Ostoja-Starzewski is proposed. On the basis of the theory, the Schrödinger equation and the energy spectrum for the quantum LC circuit were derived. By introducing special forms of position-dependent LC-electric components, the ass...

Superconductivity is analysed based on the product-like fractal measure approach with fractal dimension α introduced by Li and Ostoja-Starzewski in their attempt to explore anisotropic fractal elastic media. Our study shows the emergence of a massless state at the boundary of the superconductor and the simultaneous occurrence of isothermal and adia...

In this paper, the sharp Hille-type oscillation criteria are proposed for a class of second-order nonlinear functional dynamic equations on an arbitrary time scale, by using the technique of Riccati transformation and integral averaging method. The obtained results demonstrate an improvement in Hille-type compared with the results reported in the l...

In this study, a quantum mechanical system characterized by the product-like fractal geometry constructed by Li and Ostoja-Starzewski in order to explore physical properties of porous and anisotropic media and a position-dependent mass is constructed. We have derived the modified Schrödinger equation and we have discussed some of its main consequen...

In this study, we have constructed a viable cosmological model characterized by the presence of the Gauss–Bonnet four-dimensional invariant, higher-order corrections to the low energy effective action motivated from heterotic superstring theory and a general exponential potential comparable to those obtained in higher dimensional supergravities. Th...

In this study, we join the concept of fractality introduced by Li and Ostoja-Starzewski with the concept of nonlocality to produce a new set of nonlocal fractal fluid equations of motion. Both the unsteady and steady laminar flows are discussed. It is revealed that a damped wave equation emerges from the nonlocal fractal Navier–Stokes equation, a r...

We discuss the possibility of connecting Bateman’s approach to the concept of maximal acceleration in quantum theory. We show that if such a correlation exists, for very large acceleration or for very large time, waves propagate in atemporal space. This suggests that string theory is a limiting case of an underlying theory.