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The Functional Integral
We formulate the functional integration for Hamiltonian evolution first in quantum mechanics which can be considered as quantum field theory in one...
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Theoretical and numerical analysis of a first-kind linear Volterra functional integral equation with weakly singular kernel and vanishing delay
In this study, we investigate the existence and uniqueness of a solution for a first-kind linear Volterra functional integral equation with...
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Vallée-Poussin theorem for fractional functional differential equations with integral boundary condition
This research paper focuses on the study of a Riemann-Liouville fractional functional differential equation and a linear continuous operator acting...
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The exact solutions of conformable time-fractional modified nonlinear Schrödinger equation by first integral method and functional variable method
Using the first integral method (FIM) and the functional variable method (FVM), firstly we find the analytical solutions of conformable...
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On Hyers-Ulam-Rassias Stability of a Volterra-Hammerstein Functional Integral Equation
The aim of this paper is to study the Hyers-Ulam-Rassias stability for a Volterra-Hammerstein functional integral equation in three variables via...
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A Numerical Approach Based on Modified Lucas Wavelets for Functional Variational Problems Through Integral Operational Matrix
The present work introduces an approximated numerical technique for functional variational problems (FVPs) with mixed boundary conditions which are...
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On Chandrasekhar functional integral inclusion and Chandrasekhar quadratic integral equation via a nonlinear Urysohn–Stieltjes functional integral inclusion
We investigate the existence of solutions for a nonlinear integral inclusion of Urysohn–Stieltjes type. As applications, we give a Chandrasekhar...
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Identifying anomalous patterns in ecological communities’ diversity: leveraging functional boxplots and clustering of normalized Hill’s numbers and their integral functions
Diversity is fundamental in many disciplines, such as ecology, business, biology, and medicine. From a statistical perspective, calculating a measure...
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On refined rational convex contractions with applications to matrix and implicit functional integral equations
This research presents an advancement in fixed point theory by extending the renowned Banach contractive condition and introducing the new convex...
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Admissible Integral Manifolds for Partial Neutral Functional-Differential Equations
We prove the existence and attraction property for admissible invariant unstable and center-unstable manifolds of admissible classes of solutions to...
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Piecewise Linear Price Function of a Differential Game with Simple Dynamics and Integral Terminal Price Functional
In this paper, we consider an antagonistic differential game of two persons with dynamics described by a differential equation with simple motions...
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Application of fixed point theorem on the study of the existence of solutions in some fractional stochastic functional integral equations
In this paper, the conditions for the existence of a solution for fractional stochastic functional integral in Banach space are investigated. For...
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Inverse Source Problem for the Subdiffusion Equation on a Metric Star Graph with Integral Overdetermination Condition
AbstractIn this article, it is investigated the inverse source problem for the subdiffusion equation on the metric star graph in Sobolev space with...
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Existence results for the families of multi-map**s with applications to integral and functional equations
The aim of this manuscript is to prove some new fixed-point results for the two families of multivalued dominated-contractive maps defined on a...
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Equation of State of Materials
Equation of state (EOS)—a macroscopic representation of the thermodynamic state of materials under static and shock compression, is amongst the most...
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Classification and Applications of Randomized Functional Numerical Algorithms for the Solution of Second-Kind Fredholm Integral Equations
Systematization of numerical randomized functional algorithms for approximation of solutions to second-kind Fredholm integral equation is performed...
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Solving Einstein’s Equation
Solving Einstein’s Equation is an important problem in general relativity. Many exact solutions play important roles in the study and development of...
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Numerical methods for forward fractional Feynman–Kac equation
Fractional Feynman–Kac equation governs the functional distribution of the trajectories of anomalous diffusion. The non-commutativity of the integral...
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Reguera and Rubi Kinetic Equation
This chapter is devoted to the in-depth study of the mesoscopic non-equilibrium thermodynamics theory in the presence of entropic barriers, as well...
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A Difference Scheme for Wave Equation
AbstractThe paper deals with a numerical solution of a wave equation. The solution algorithm uses optimal parameters which are obtained by using...
