Papers by Praveen Agarwal
Open Physics
The main aim of this article is to study a new generalizations of the Gauss hypergeometric matrix... more The main aim of this article is to study a new generalizations of the Gauss hypergeometric matrix and confluent hypergeometric matrix functions by using two-parameter Mittag–Leffler matrix function. In particular, we investigate certain important properties of these extended matrix functions such as integral representations, differentiation formulas, beta matrix transform, and Laplace transform. Furthermore, we introduce an extension of the Jacobi matrix orthogonal polynomial by using our generalized Gauss hypergeometric matrix function, which is very important in scattering theory and inverse scattering theory.
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Advances in Difference Equations, 2021
We study a conformable fractional nonlocal thermistor problem on time scales. Under an appropriat... more We study a conformable fractional nonlocal thermistor problem on time scales. Under an appropriate nonrestrictive condition on the resistivity function, we establish existence and uniqueness results. The proof is based on the use of Schauder’s point fixed theorem.
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Mathematics, 2022
The main aim of this article is to study an extension of the Beta and Gamma matrix functions by u... more The main aim of this article is to study an extension of the Beta and Gamma matrix functions by using a two-parameter Mittag-Leffler matrix function. In particular, we investigate certain properties of these extended matrix functions such as symmetric relation, integral representations, summation relations, generating relation and functional relation.
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Entropy, 2021
We extend the operational matrices technique to design a spectral solution of nonlinear fractiona... more We extend the operational matrices technique to design a spectral solution of nonlinear fractional differential equations (FDEs). The derivative is considered in the Caputo sense. The coupled system of two FDEs is considered, subjected to more generalized integral type conditions. The basis of our approach is the most simple orthogonal polynomials. Several new matrices are derived that have strong applications in the development of computational scheme. The scheme presented in this article is able to convert nonlinear coupled system of FDEs to an equivalent S-lvester type algebraic equation. The solution of the algebraic structure is constructed by converting the system into a complex Schur form. After conversion, the solution of the resultant triangular system is obtained and transformed back to construct the solution of algebraic structure. The solution of the matrix equation is used to construct the solution of the related nonlinear system of FDEs. The convergence of the proposed...
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Mathematics, 2021
In this manuscript, some tripled fixed point results were derived under (φ,ρ,ℓ)-contraction in th... more In this manuscript, some tripled fixed point results were derived under (φ,ρ,ℓ)-contraction in the framework of ordered partially metric spaces. Moreover, we furnish an example which supports our theorem. Furthermore, some results about a homotopy results are obtained. Finally, theoretical results are involved in some applications, such as finding the unique solution to the boundary value problems and homotopy theory.
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Advances in Difference Equations, 2021
Fractional calculus is the field of mathematical analysis that investigates and applies integrals... more Fractional calculus is the field of mathematical analysis that investigates and applies integrals and derivatives of arbitrary order. Fractional q-calculus has been investigated and applied in a variety of research subjects including the fractional q-trapezoid and q-midpoint type inequalities. Fractional $(p,q)$ ( p , q ) -calculus on finite intervals, particularly the fractional $(p,q)$ ( p , q ) -integral inequalities, has been studied. In this paper, we study two identities for continuous functions in the form of fractional $(p,q)$ ( p , q ) -integral on finite intervals. Then, the obtained results are used to derive some fractional $(p,q)$ ( p , q ) -trapezoid and $(p,q)$ ( p , q ) -midpoint type inequalities.
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arXiv: Classical Analysis and ODEs, 2017
Hypergeometric functions and their generalizations play an important r\^{o}les in diverse applica... more Hypergeometric functions and their generalizations play an important r\^{o}les in diverse applications. Many authors have been established generalizations of hypergeometric functions by a number ways. In this paper, we aim at establishing (presumably new) extended $k-$type hypergeometric function $_{2}f_{1}^{k}[a, b; c; \omega; z]$ and study various properties including integral representations, differential formulas and fractional integral and derivative formula.
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Symmetry, 2021
Eco-epidemiological can be considered as a significant combination of two research fields of comp... more Eco-epidemiological can be considered as a significant combination of two research fields of computational biology and epidemiology. These problems mainly take ecological systems into account of the impact of epidemiological factors. In this paper, we examine the chaotic nature of a computational system related to the spread of disease into a specific environment involving a novel differential operator called the Atangana–Baleanu fractional derivative. To approximate the solutions of this fractional system, an efficient numerical method is adopted. The numerical method is an implicit approximate method that can provide very suitable numerical approximations for fractional problems due to symmetry. Symmetry is one of the distinguishing features of this technique compared to other methods in the literature. Through considering different choices of parameters in the model, several meaningful numerical simulations are presented. It is clear that hiring a new derivative operator greatly ...
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Symmetry, 2021
In this research study, we establish some necessary conditions to check the uniqueness-existence ... more In this research study, we establish some necessary conditions to check the uniqueness-existence of solutions for a general multi-term ψ-fractional differential equation via generalized ψ-integral boundary conditions with respect to the generalized asymmetric operators. To arrive at such purpose, we utilize a procedure based on the fixed-point theory. We follow our study by suggesting two numerical algorithms called the Dafterdar-Gejji and Jafari method (DGJIM) and the Adomian decomposition method (ADM) techniques in which a series of approximate solutions converge to the exact ones of the given ψ-RLFBVP and the equivalent ψ-integral equation. To emphasize for the compatibility and the effectiveness of these numerical algorithms, we end this investigation by providing some examples showing the behavior of the exact solution of the existing ψ-RLFBVP compared with the approximate ones caused by DGJIM and ADM techniques graphically.
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Mathematics, 2020
Various k-special functions such as k-gamma function, k-beta function and k-hypergeometric functi... more Various k-special functions such as k-gamma function, k-beta function and k-hypergeometric functions have been introduced and investigated. Recently, the k-gamma function of a matrix argument and k-beta function of matrix arguments have been presented and studied. In this paper, we aim to introduce an extended k-gamma function of a matrix argument and an extended k-beta function of matrix arguments and investigate some of their properties such as functional relations, inequality, integral formula, and integral representations. Also an application of the extended k-beta function of matrix arguments to statistics is considered.
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Advances in Difference Equations, 2020
In this article, a fractional-order mathematical physics model, advection–dispersion equation (FA... more In this article, a fractional-order mathematical physics model, advection–dispersion equation (FADE), will be solved numerically through a new approximative technique. Shifted Vieta–Lucas orthogonal polynomials will be considered as the main base for the desired numerical solution. These polynomials are used for transforming the FADE into an ordinary differential equations system (ODES). The nonstandard finite difference method coincidence with the spectral collocation method will be used for converting the ODES into an equivalence system of algebraic equations that can be solved numerically. The Caputo fractional derivative will be used. Moreover, the error analysis and the upper bound of the derived formula error will be investigated. Lastly, the accuracy and efficiency of the proposed method will be demonstrated through some numerical applications.
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Symmetry, 2021
In this paper, we intorduce a family of analytic functions in the open unit disk which is bi-univ... more In this paper, we intorduce a family of analytic functions in the open unit disk which is bi-univalent. By the virtue of the Faber polynomial expansions, the estimation of n−th(n≥3) Taylor–Maclaurin coefficients an is obtained. Furthermore, the bounds value of the first two coefficients of such functions is established.
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Boletim da Sociedade Paranaense de Matemática, 2021
The aim of this paper is to evaluate two theorems for fractional integration involving Appell’s f... more The aim of this paper is to evaluate two theorems for fractional integration involving Appell’s function due to Marichev-Saigo-Maeda, to the product of the generalized Bessel-Maitland function. The results are expressed in terms of the multivariable generalized Lauricella functions. Corresponding assertions in terms of Saigo, Erdẻlyi-Kober, Riemann-Liouville, and Weyl type of fractional integrals are also presented. Some interesting special cases of our two main results are presented. Further, we point out also their relevance
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Boundary behavior of a given important function or its limit values are essential in the whole sp... more Boundary behavior of a given important function or its limit values are essential in the whole spectrum of mathematics and science. We consider some tractable cases of limit values in which either a difference of two ingredients or a difference equation is used coupled with the relevant functional equations to give rise to unexpected results. This involves the expression for the Laurent coefficients including the residue, the Kronecker limit formulas and higher order coefficients as well as the difference formed to cancel the inaccessible part, typically the Clausen functions. We also state Abelian results which yield asymptotic formulas for weighted summatory function from that for the original summatory function
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Journal of Nonlinear Sciences and Applications, 2016
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Advances in Difference Equations, 2018
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International Journal of Applied and Computational Mathematics, 2018
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Communications of the Korean Mathematical Society, 2017
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Journal of Mathematical Inequalities, 2016
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Papers by Praveen Agarwal
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