29,375 Results Found

This paper deals with a general class of integrals, the particular cases of which are connected to outstanding problems in physics and astronomy. Nuclear reaction rate probability integrals in nuclear physics, Krätzel integrals in applied mathem...

The main aim of this article is to study the Fredholm-type integral equation involving the incomplete H-function (IHF) and incomplete H-function in the kernel. Firstly, we solve an integral equation associated with the IHF with the aid of the theory...

In the present paper, a new special function, the so-called extreme value $\mathbb{H}$-function, is introduced. This new function, which is a generalization of the H-function with a particular set of parameters, appears while dealing with products and quotients...

Needed for cosmological and stellar nucleosynthesis, we are studying the closed-form analytic evaluation of thermonuclear reaction rates. In this context, we undertake a comprehensive analysis of three largely distinct velocity distributions, namely...

A fractional calculus concept is considered in the framework of a Volterra type integro-differential equation, which is employed for the self-consistent description of the high-gain free-electron laser (FEL). It is shown that the Fox H-function is th...

The objective of this research is to obtain some fractional integral formulas concerning products of the generalized Mittag–Leffler function and two H-functions. The resulting integral formulas are described in terms of the H-function of severa...

In this paper, we established some interesting integrals associated with the product of M-series and incomplete H-functions, which are expressed in terms of incomplete H-functions. Next, we give some special cases by specializing the parameters of M-...

In the present scenario, coherent states of a quantum harmonic oscillator are generalized with positive Fox H auxiliary functions. The novel generalized coherent states provide canonical coherent states and Mittag-Leffler or Wright generalized cohere...

In this paper, the pathway model for the real scalar variable case is re-explored and its connections to fractional integrals, solutions of fractional differential equations, Tsallis statistics and superstatistics in statistical mechanics, the reacti...

In this paper, we consider fractional ordinary differential equations and the fractional Euler–Poisson–Darboux equation with fractional derivatives in the form of a power of the Bessel differential operator. Using the technique of the Meijer integral...

In this paper, we consider generalized space-time fractional cable equation in presence of external source. By using the Fourier-Laplace transform we obtain the Green function in terms of infinite series in H-functions. The fractional moments of the...

The problem of target detection in impulsive non-Gaussian sea clutter has attracted a lot of attention in recent years. The positive alpha-stable (PαS) distribution has been validated as a suitable model for the impulsive non-Gaussian sea clutt...

The closed forms of the non-resonant thermonuclear function in the Maxwell–Boltzmann and Tsallis case with depleted tail are obtained in generalized special functions. The results are written in terms of H-function of two variables. The importance of...

In the survey Kiryakova: “A Guide to Special Functions in Fractional Calculus” (published in this same journal in 2021) we proposed an overview of this huge class of special functions, including the Fox H-functions, the Fox–Wright g...

The decomposition of a point process is useful for the analysis of spatial patterns and in the discovery of potential mechanisms of geographic phenomena. However, when a local repulsive cluster is present in a complex heterogeneous point process, the...

In this paper, the definition of the harmonically $cr$-h-convex function is given, and its important properties are discussed. Jensen type inequality, Hermite–Hadamard type inequalities and Fejér type inequalities for harmonically $cr$-h-con...

the present paper we evaluate a number of key Eulerian integrals involving the H- function of several complex variables. Our general Eulerian integral formulas are shown to provide the key formulae from which numerous other potentially useful results...

This paper studies the design problem of fault detection (FD) observer for unmanned marine vehicles (UMVs) based on the T-S fuzzy model. Firstly, T-S fuzzy systems are used to approximate the nonlinear dynamics in UMVs. Secondly, to improve the FD pe...

This paper introduces extensions $H_{4,p}$ and $X_{8,p}$ of Horn’s double hypergeometric function $H_4$ and Exton’s triple hypergeometric function $X_8$, taking into account recent extensions of Euler’s beta function, hypergeometric function, and c...

The diabetic heart is characterized by a shift in substrate utilization from glucose to lipids, which may ultimately lead to contractile dysfunction. This substrate shift is facilitated by increased translocation of lipid transporter CD36 (SR-B2) fro...

Integral inequalities involving many fractional integral operators are used to solve various fractional differential equations. In the present paper, we will generalize the Hermite–Jensen–Mercer-type inequalities for an h-convex function...

Elevated homocysteine (Hcy) increases cardiovascular disease (CVD) risk. Our objective was to emphasize Hcy’s contribution in hypertension and CVD management by determining H-type hypertension (hypertension with Hcy ≥ 10 µmol/L) and as...

Cognitive decline can result from various factors, including direct neurotoxic injury, brain tissue damage, inflammation, and disruptions in coagulation and fibrinolysis. This study aimed to examine the relationship between biochemical markers associ...

Age-related macular degeneration (AMD), the leading cause of vision loss in the elderly, is characterized by loss of the retinal pigment epithelium (RPE). While the disease mechanism remains unclear, prior studies have linked AMD with RPE mitochondri...

In passive microwave remote sensing, mirrored aperture synthesis (MAS) demonstrates significant potential for atmospheric observation from geostationary orbit. The amplitude and phase errors are among the key factors that degrade image reconstruction...

This paper is devoted to the study of the multi-dimensional integral transform with the Fox H-function in the kernel in weighted spaces with integrable functions in the domain ${\mathbb{R}}_{+}^n$ with positive coordinates. Due to the generality of the Fox H-function...

This article deals with some variants of Krätzel integral operators involving Fox’s H-function and their extension to classes of distributions and spaces of Boehmians. For real numbers a and $b>0$ , the Fréchet space $H_{}$...

The heart is metabolically flexible. Under physiological conditions, it mainly uses lipids and glucose as energy substrates. In uncontrolled diabetes, the heart switches towards predominant lipid utilization, which over time is detrimental to cardiac...

In a joint paper with Srivastava and Chopra, we introduced far-reaching generalizations of the extended Gammafunction, extended Beta function and the extended Gauss hypergeometric function. In this present paper, we extend the generalized Mittag–Leff...

A stable water-in-oil Pickering emulsion was fabricated with SO₃H-functionalized ionic liquid and surface-modified silica nanoparticles and used for 2,2′-(4-nitrophenyl) dipyrromethane synthesis in a packed-bed microreactor, exhibiting high reaction...

In recent years, transition metal-catalyzed C–H activation and site-selective functionalization have been considered to be valuable synthetic tactics to functionalize organic compounds containing multiple C–H bonds. Pyrene is one of the p...

Our goal in this paper is to generalize the class of additive functions to a more general class of functions, h-additive functions, and give several characterizations of this class by using its symmetry. Also, we provide a definition of this class of...

In this paper, we prove the Hermite–Hadamard–Fejér type inequalities for coordinated $\left(h_1,h_2\right)$-convex functions on the rectangle from the plane ${\mathbb{R}}^2$. Some generalizations of the Hermite–Hadamard-type inequalities of two variables a...

Symmetry is a fascinating property of numerous mathematical notions. In mathematical analysis a function $f:[a,b]\to \mathbf{R}$ symmetric about $\frac{a+b}{2}$ satisfies the equation $f(a+b-x)=f\left(x\right)$. In this paper, we investigate the relationship of unified Mittag&...

We introduce the concept of interval $(h_1,h_2)$ -convex functions. Under the new concept, we establish some new interval Hermite-Hadamard type inequalities, which generalize those in the literature. Also, we give some interesting examples.

In the theory of special functions, finding correlations between different types of functions is of great interest as unifying results, especially when considering issues such as analytic continuation. In the present paper, the relation between Lambe...

In this paper, we consider and study in detail the generalized Fox–Wright function ${}_p\tilde{\Psi }_q$ introduced in our recent work as an extension of the Fox–Wright function ${}_p\Psi _q$. This special function can be seen as an important case of...

Using Mellin-Barnes contour integrals, we aim at suggesting a q-analogue (q-extension) of the several variable Aleph-function. Then we present Riemann Liouville fractional q-integral and q-differential formulae for the q-extended several variable Ale...

The idea that entropy is associated with the “arrow of time” has its roots in Clausius’s statement on the Second Law: “Entropy of the Universe always increases.” However, the explicit association of the entropy with time...

This article is in continuation of the authors research attempts to derive computational solutions of an unified reaction-diffusion equation of distributed order associated with Caputo derivatives as the time-derivative and Riesz-Feller derivative as...

A comb model with periodic potential in side branches is introduced. A comb model is a model of geometrically constrained diffusion, such that the diffusion process along the comb’s main axis (backbone) is coupled to the diffusion process in fi...

In this study, the Hermite–Hadamard–Fejér inequalities for $GA$-h-convex are proved, and the results for particular classes of functions are highlighted. In addition, several generalizations of the Hermite–Hadamard inequalities...

In this article, firstly, we establish a novel definition of weighted interval-valued fractional integrals of a function $\breve{\mathsf{{\rm Y}}}$ using an another function $\vartheta \left(\dot{\zeta }\right)$. As an additional observation, it is noted that the new class of weighted interval-valued frac...

Wild-type p53 is known as “the guardian of the genome” because of its function of inducing DNA repair, cell-cycle arrest, and apoptosis, preventing the accumulation of gene mutations. TP53 is highly mutated in cancer cells and most TP53 hotspot mutat...

In this article, we demonstrated various Hermite–Hadamard and Fejér type inequalities for modified h-convex functions. We showed several inequalities for the products of two modified h-convex functions. New identities related to inequali...

On the one hand, convex functions are important to derive rigorous convergence rates, and on the other, synchronous functions are significant to solve statistical problems using Chebyshev inequalities. Therefore, fractional integral inequalities invo...

Many researchers have been attracted to the study of convex analysis theory due to both facts, theoretical significance, and the applications in optimization, economics, and other fields, which has led to numerous improvements and extensions of the s...

Pea albumin is a high-quality plant-based protein with growing relevance in food applications, yet the effects of pH and thermal treatment on its structural and functional properties remain insufficiently understood. This study investigated the effec...

Firstly, a basic question to find the Laplace transform using the classical representation of gamma function makes no sense because the singularity at the origin nurtures so rapidly that $\mathsf{\Gamma }\left(\mathrm{z}\right){\mathrm{e}}^{-\mathrm{s}\mathrm{z}}$ cannot be integrated over positive real numb...

Combs are a simple caricature of various types of natural branched structures, which belong to the category of loopless graphs and consist of a backbone and branches. We study two generalizations of comb models and present a generic method to obtain...