Devendra Kumar
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View article: On the solutions of generalized Cauchy differential equations and diffusion equations with k-Hilfer-Prabhakar derivative
On the solutions of generalized Cauchy differential equations and diffusion equations with k-Hilfer-Prabhakar derivative Open
In this article, natural transform of k-Prabhakar integral, k-Prabhakar derivative, k-Hilfer-Prabhakar fractional derivative (k-HPFD) are calculated. In addition, we also obtain the natural transform of regularized versions of k-Prabhakar …
View article: An efficient numerical method for fractional order nonlinear two-point boundary value problem occurring in chemical reactor theory
An efficient numerical method for fractional order nonlinear two-point boundary value problem occurring in chemical reactor theory Open
This paper is focused on computing an approximate numerical solution of the strongly nonlinear multi-order fractional version (SNMOFV) of a BVP that appears in the theory of chemical reactors. The fractional derivative is defined by using …
View article: PREFACE: SPECIAL ISSUE ON RECENT DEVELOPMENTS ON THE FRACTAL AND FRACTIONAL CALCULUS IN PHYSICS AND CIRCUITS AND SYSTEMS — PART II
PREFACE: SPECIAL ISSUE ON RECENT DEVELOPMENTS ON THE FRACTAL AND FRACTIONAL CALCULUS IN PHYSICS AND CIRCUITS AND SYSTEMS — PART II Open
View article: Fractional Calculus Approach for Variational Problems: Characterization of Sufficient Optimality Conditions and Duality
Fractional Calculus Approach for Variational Problems: Characterization of Sufficient Optimality Conditions and Duality Open
In this paper, we present a Wolfe-type dual model containing the Caputo-Fabrizio fractional derivative, weak and strong duality results, number of Kuhn-Tucker type sufficient optimality conditions and duality results for variational proble…
View article: On Efficient Method For Fractional-Order Two-Dimensional Navier-Stokes Equations
On Efficient Method For Fractional-Order Two-Dimensional Navier-Stokes Equations Open
For the solution of fractional-order two-dimensional Navier-Stokes equations (FOTDNSEs), the current work proposes a novel variant of the Laplace Adomian decomposition approach with the Atangana-Baleanu fractional operator in the Caputo se…
View article: A reliable computational approach for fractional isothermal chemical model
A reliable computational approach for fractional isothermal chemical model Open
This article analyzes and computes numerical solutions for the fractional isothermal chemical (FIC) model. This work suggested a Jacobi collocation method (JCM) to examine the FIC model. In the beginning, we constructed the operational mat…
View article: A mathematical theoretical study of Atangana-Baleanu fractional Burgers’ equations
A mathematical theoretical study of Atangana-Baleanu fractional Burgers’ equations Open
In this paper, the Burgers’ equations using the fractional derivative of Atangana-Baleanu sense are investigated and discussed. A Laplace variational iteration approach is used to demonstrate the fractional model's mathematical solution. T…
View article: Analytical solution of fuzzy heat problem in two-dimensional case under Caputo-type fractional derivative
Analytical solution of fuzzy heat problem in two-dimensional case under Caputo-type fractional derivative Open
This work aims to investigate the analytical solution of a two-dimensional fuzzy fractional-ordered heat equation that includes an external diffusion source factor. We develop the Sawi homotopy perturbation transform scheme (SHPTS) by merg…
View article: An Efficient Numerical Scheme for Fractional Order Mathematical Model of Cytosolic Calcium Ion in Astrocytes
An Efficient Numerical Scheme for Fractional Order Mathematical Model of Cytosolic Calcium Ion in Astrocytes Open
The major aim of this article is to obtain the numerical solution of a fractional mathematical model with a nonsingular kernel for thrombin receptor activation in calcium signals using two numerical schemes based on the collocation techniq…
View article: A robust approach for computing solutions of fractional-order two-dimensional Helmholtz equation
A robust approach for computing solutions of fractional-order two-dimensional Helmholtz equation Open
In ocean engineering, the Helmholtz equation plays a crucial role in the study of wave propagation, underwater acoustics, and the behavior of waves in the ocean environment. The equation is used to describe how waves, such as sound waves o…
View article: Genetic diversity, population structure analysis and codon substitutions of Indicine Badri cattle using ddRAD sequencing
Genetic diversity, population structure analysis and codon substitutions of Indicine Badri cattle using ddRAD sequencing Open
View article: Fractional dynamics and computational analysis of food chain model with disease in intermediate predator
Fractional dynamics and computational analysis of food chain model with disease in intermediate predator Open
In this paper, a fractional food chain system consisting of a Holling type Ⅱ functional response was studied in view of a fractional derivative operator. The considered fractional derivative operator provided nonsingular as well as a nonl…
View article: Dynamical and computational analysis of a fractional predator-prey model with an infectious disease and harvesting policy
Dynamical and computational analysis of a fractional predator-prey model with an infectious disease and harvesting policy Open
This paper examined the features of an infection therapy for fractional-order quarry-hunter systems in order to control sickness. It focused especially on how illnesses and several populations combine to affect how well harvesting policies…
View article: A RELIABLE NUMERICAL ALGORITHM FOR TREATMENT OF FRACTIONAL MODEL OF CONVECTIVE STRAIGHT FINS WITH TEMPERATURE DEPENDENT THERMAL CONDUCTIVITY
A RELIABLE NUMERICAL ALGORITHM FOR TREATMENT OF FRACTIONAL MODEL OF CONVECTIVE STRAIGHT FINS WITH TEMPERATURE DEPENDENT THERMAL CONDUCTIVITY Open
Fins serve the purpose of enhancing heat transfer between their surroundings and the underlying surface, resembling the function of heat exchangers in various scientific domains. This research undertakes an investigation into the temperatu…
View article: Computational analysis of fractional Michaelis-Menten enzymatic reaction model
Computational analysis of fractional Michaelis-Menten enzymatic reaction model Open
In this study for examining the fractional Michaelis-Menten enzymatic reaction (FMMER) model, we suggested a computational method by using an operational matrix of Jacobi polynomials (JPs) as its foundation. We obtain an operational matrix…
View article: Numerical analysis for MHD blood-nanofluid flow through a non-linearly stretched sheet interpolated in a permeable medium along heat generation
Numerical analysis for MHD blood-nanofluid flow through a non-linearly stretched sheet interpolated in a permeable medium along heat generation Open
In this study, steady and incompressible MHD movement of a viscous nanofluid past a non-linear stretching plate has been investigated mathematically by considering heat generation. Blood is employed as the base fluid. Mathematical modeling…
View article: Numerical and computational analysis of fractional order mathematical models for chemical kinetics and carbon dioxide absorbed into phenyl glycidyl ether
Numerical and computational analysis of fractional order mathematical models for chemical kinetics and carbon dioxide absorbed into phenyl glycidyl ether Open
The major objective of this effort is to use the collocation technique (CT) to examine fractional chemical kinetics(CK) and other problem that correlates the condensations of carbon dioxide (CO2) and phenyl glycidyl ether (PGE) with two va…
View article: Anisotropic Magnetized String model with Constant Decelerating Parameter in General Theory of Relativity
Anisotropic Magnetized String model with Constant Decelerating Parameter in General Theory of Relativity Open
Cosmological model in the presence of cloud strings with electro- magnetic field in general theory of relativity. Exact solutions of field equations are obtained using the fact that shear scalar is proportional to scalar expansion and cons…
View article: Analysis of Cauchy Problems and Diffusion Equations Associated with the Hilfer–Prabhakar Fractional Derivative via Kharrat–Toma Transform
Analysis of Cauchy Problems and Diffusion Equations Associated with the Hilfer–Prabhakar Fractional Derivative via Kharrat–Toma Transform Open
In this paper, the Kharrat–Toma transforms of the Prabhakar integral, a Hilfer–Prabhakar (HP) fractional derivative, and the regularized version of the HP fractional derivative are derived. Moreover, we also compute the solution of some Ca…
View article: Regularization of Nonlocal Pseudo-Parabolic Equation with Random Noise
Regularization of Nonlocal Pseudo-Parabolic Equation with Random Noise Open
In this paper, we consider an inverse problem for a time-fractional diffusion equation with the inhomogeneous source. These problems have many applications in engineering such as image processing, geophysics, biology. We get the result in …
View article: Analysis of Fuzzy Differential Equation with Fractional Derivative in Caputo Sense
Analysis of Fuzzy Differential Equation with Fractional Derivative in Caputo Sense Open
In this article, the dynamics of the fuzzy fractional order enzyme Michaelis Menten model are investigated. To study problems with uncertainty, fuzzy fractional technique is applied. Using fuzzy theory, the sequential iterations of the mod…
View article: Genome-wide association study revealed suggestive QTLs for production and reproduction traits in Indian Murrah buffalo
Genome-wide association study revealed suggestive QTLs for production and reproduction traits in Indian Murrah buffalo Open
View article: Computational Analysis of the Fractional Riccati Differential Equation with Prabhakar-type Memory
Computational Analysis of the Fractional Riccati Differential Equation with Prabhakar-type Memory Open
The key objective of the current work is to examine the behavior of the nonlinear fractional Riccati differential equation associated with the Caputo–Prabhakar derivative. An efficient computational scheme, that is, a mixture of homotopy a…
View article: Regularity for a non-local diffusion equation with Riemann-Liouville derivative
Regularity for a non-local diffusion equation with Riemann-Liouville derivative Open
Our main goal in this paper is to investigate the regularity of the mild solution fractional diffusion equation which can be used in the modelling of heat transfer with memory effects. Under some various assumptions of the input data, we o…
View article: Analysis of the impact of thermal radiation and velocity slip on the melting of magnetic hydrodynamic micropolar fluid-flow over an exponentially stretching sheet
Analysis of the impact of thermal radiation and velocity slip on the melting of magnetic hydrodynamic micropolar fluid-flow over an exponentially stretching sheet Open
The belongings of radiation and velocity slip on MHD stream and melting warmth transmission of a micropolar liquid over an exponentially stretched sheet which is fixed in a porous medium with heat source/sink are accessible. Homothety tran…
View article: Identifying of unknown source term for the Rayleigh-Stokes problem
Identifying of unknown source term for the Rayleigh-Stokes problem Open
In this paper, we would like to briefly introduce some applications of fractional derivatives in the fields of heat and fluid-flows. However, our main focus is on study an inverse source problem for the Rayleigh-Stokes problem. The problem…
View article: Computational Analysis of Fractional Diffusion Equations Occurring in Oil Pollution
Computational Analysis of Fractional Diffusion Equations Occurring in Oil Pollution Open
The fractional model of diffusion equations is very important in the study of oil pollution in the water. The key objective of this article is to analyze a fractional modification of diffusion equations occurring in oil pollution associate…
View article: Groundwater flow in karstic aquifer: analytic solution of dual-porosity fractional model to simulate groundwater flow
Groundwater flow in karstic aquifer: analytic solution of dual-porosity fractional model to simulate groundwater flow Open
Karst aquifers have a very complex flow system because of their high spatial heterogeneity of void distribution. In this manuscript, flow simulation has been used to investigate the flow mechanism in a fissured karst aquifer with double po…
View article: Computational Analysis of Local Fractional LWR Model Occurring in a Fractal Vehicular Traffic Flow
Computational Analysis of Local Fractional LWR Model Occurring in a Fractal Vehicular Traffic Flow Open
In this paper, we implement computational methods, namely the local fractional natural homotopy analysis method (LFNHAM) and local fractional natural decomposition method (LFNDM), to examine the solution for the local fractional Lighthill–…
View article: Guest Editors
Guest Editors Open