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Papers by Rajendra Bairwa

Research paper thumbnail of An efficient computational technique for solving the Fokker–Planck equation with space and time fractional derivatives

Journal of King Saud University - Science, 2016

Research paper thumbnail of Analytical Approach to Fractional Order Newell-Whitehead-Segel Equations by Sumudu transform Iterative Method

JOURNAL OF INTERNATIONAL ACADEMY OF PHYSICAL SCIENCES

The present paper aims to solve the linear and nonlinear time-fractional Newell-Whitehead-Segel e... more The present paper aims to solve the linear and nonlinear time-fractional Newell-Whitehead-Segel equations using the Sumudu transformiterative method. The time-fractional derivatives areconsidered in the Caputo sense.In addition, the approximate analytical solutions derived in series form are graphically represented in this investigation, and the solution graphs show that the approximate solution is closely related to the exact solution

Research paper thumbnail of Analytical Solutions for Time-Fractional Cauchy Reaction-Diffusion Equations Using Iterative Laplace Transform Method

Jnanabha

In the present work, the iterative Laplace transform method (ILTM) is implemented to derive appro... more In the present work, the iterative Laplace transform method (ILTM) is implemented to derive approximate analytical solutions for the time-fractional Cauchy reaction-diffusion equations (CRDEs) within the Caputo fractional derivative. The proposed technique is an elegant amalgam of the Iterative method and the Laplace transform method. The ILTM produces the solution in a rapid convergent series which may lead to the solution in a closed form. The obtained analytical outcomes with the help of the proposed technique are examined graphically.

Research paper thumbnail of Certain Properties of Generalized q-Mittag–Leffler Type Function and its Application in Fractional q-Kinetic Equation

International Journal of Applied and Computational Mathematics

Research paper thumbnail of Solution of the Quadratic Integral Equation by Homotopy Analysis Method

Annals of Pure and Applied Mathematics

In the present paper, we derive an approximate solution of the quadratic integral equation by usi... more In the present paper, we derive an approximate solution of the quadratic integral equation by using the homotopy analysis method (HAM). This approach provides a solution in the form of a rapidly converging series, and it includes an auxiliary parameter that controls the series solution's convergence. We compare the HAM solution with the exact solution graphically. Additionally, an absolute error comparison between the exact and HAM solutions is performed. The findings indicate that HAM is a very straightforward and attractive approach for computation.

Research paper thumbnail of Pathway Fractional Integral Operator on Some τ-extensions of Lauricella Functions of Several Variables

Journal of Mathematics and Informatics, 2021

In this paper, we establish new results as images of τ-extensions of Lauricella functions of seve... more In this paper, we establish new results as images of τ-extensions of Lauricella functions of several variables using the pathway fractional integral operator. The pathway fractional integral operator's motivation is a switching mechanism that transforms one fractional form to another with important applications. Some interesting special cases of our main findings are also highlighted.

Research paper thumbnail of Annals of A Reliable Treatment of Iterative Laplace Transform Method for Fractional Telegraph Equations

Abstract. In this paper a reliable algorithm for the iterative Laplace transform method (ILTM) is... more Abstract. In this paper a reliable algorithm for the iterative Laplace transform method (ILTM) is presented. ILTM is a combination of Laplace transform method and Iterative method to solve space- and time- fractional telegraph equations. The fractional derivatives are considered in Caputo sense. Closed form analytical expressions are derived in terms of the Mittag-Leffler functions. An illustrative numerical case study is presented for the proposed method to show the preciseness and effectiveness of the method.

Research paper thumbnail of A Reliable Treatment of Iterative Laplace Transform Method for Fractional Telegraph Equations

Abstract. In this paper a reliable algorithm for the iterative Laplace transform method (ILTM) is... more Abstract. In this paper a reliable algorithm for the iterative Laplace transform method (ILTM) is presented. ILTM is a combination of Laplace transform method and Iterative method to solve spaceand timefractional telegraph equations. The fractional derivatives are considered in Caputo sense. Closed form analytical expressions are derived in terms of the Mittag-Leffler functions. An illustrative numerical case study is presented for the proposed method to show the preciseness and effectiveness of the method.

Research paper thumbnail of Iterative Laplace Transform Method for Solving Fractional Heat and Wave- Like Equations

In this paper, we derive the closed form solutions of the fractional heat and wave like equations... more In this paper, we derive the closed form solutions of the fractional heat and wave like equations in terms of Mittag-Leffler functions by the use of iterative Laplace transform method. In the process the time-fractional derivatives are considered in Caputo sense for the said problem.

Research paper thumbnail of An efficient analytical approach for solving fractional Fokker-Planck equations

The present study focuses on investigating the approximate analytical solutions of linear and non... more The present study focuses on investigating the approximate analytical solutions of linear and nonlinear FokkerPlanck equations (FPEs) with spaceand time-fractional derivatives using an efficient analytical method, namely the Sumudu transform iterative method (STIM).The fractional derivatives are represented in the terms of Caputo. Analytical outcomes are obtained in the form of a converging series with easily computable components and are shown graphically. The results of the study suggest that the approach is simple to implement and very attractive in terms of computation.

Research paper thumbnail of An Efficient Computation Approach for Abel's Integral Equations of the Second Kind

This paper presents the application of a new powerful method named as q-homotopy analysis transfo... more This paper presents the application of a new powerful method named as q-homotopy analysis transform method (q-HATM). The q-HATM is a combination of the q-homotopy analysis scheme and the Laplace transform approach and more general than other existing techniques. Abel’s integral equation of the second kind has been solved by using this method. We solve some examples and plot the graphs. The numerical solutions are shown in the form of graphs.

Research paper thumbnail of • ANALYTICAL SOLUTION OF ABEL’S INTEGRAL EQUATION OF THE FIRST KIND BY USING q-HOMOTOPY ANALYSIS TRANSFORM METHOD

International Journal of Mathematical Archive EISSN 2229-5046, Jun 27, 2021

Research paper thumbnail of An Efficient Computation Approach for Abel’s Integral Equations of the Second Kind

This paper presents the application of a new powerful method named as q-homotopy analysis transfo... more This paper presents the application of a new powerful method named as q-homotopy analysis transform method (q-HATM). The q-HATM is a combination of the q-homotopy analysis scheme and the Laplace transform approach and more general than other existing techniques. Abel’s integral equation of the second kind has been solved by using this method. We solve some examples and plot the graphs. The numerical solutions are shown in the form of graphs.

Research paper thumbnail of Analytical Approach to Fractional Navier–Stokes Equations by Iterative Laplace Transform Method

Mathematical Modelling, Applied Analysis and Computation

Research paper thumbnail of An efficient computational technique for solving the Fokker–Planck equation with space and time fractional derivatives

Journal of King Saud University - Science, 2016

Research paper thumbnail of Analytical Approach to Fractional Order Newell-Whitehead-Segel Equations by Sumudu transform Iterative Method

JOURNAL OF INTERNATIONAL ACADEMY OF PHYSICAL SCIENCES

The present paper aims to solve the linear and nonlinear time-fractional Newell-Whitehead-Segel e... more The present paper aims to solve the linear and nonlinear time-fractional Newell-Whitehead-Segel equations using the Sumudu transformiterative method. The time-fractional derivatives areconsidered in the Caputo sense.In addition, the approximate analytical solutions derived in series form are graphically represented in this investigation, and the solution graphs show that the approximate solution is closely related to the exact solution

Research paper thumbnail of Analytical Solutions for Time-Fractional Cauchy Reaction-Diffusion Equations Using Iterative Laplace Transform Method

Jnanabha

In the present work, the iterative Laplace transform method (ILTM) is implemented to derive appro... more In the present work, the iterative Laplace transform method (ILTM) is implemented to derive approximate analytical solutions for the time-fractional Cauchy reaction-diffusion equations (CRDEs) within the Caputo fractional derivative. The proposed technique is an elegant amalgam of the Iterative method and the Laplace transform method. The ILTM produces the solution in a rapid convergent series which may lead to the solution in a closed form. The obtained analytical outcomes with the help of the proposed technique are examined graphically.

Research paper thumbnail of Certain Properties of Generalized q-Mittag–Leffler Type Function and its Application in Fractional q-Kinetic Equation

International Journal of Applied and Computational Mathematics

Research paper thumbnail of Solution of the Quadratic Integral Equation by Homotopy Analysis Method

Annals of Pure and Applied Mathematics

In the present paper, we derive an approximate solution of the quadratic integral equation by usi... more In the present paper, we derive an approximate solution of the quadratic integral equation by using the homotopy analysis method (HAM). This approach provides a solution in the form of a rapidly converging series, and it includes an auxiliary parameter that controls the series solution's convergence. We compare the HAM solution with the exact solution graphically. Additionally, an absolute error comparison between the exact and HAM solutions is performed. The findings indicate that HAM is a very straightforward and attractive approach for computation.

Research paper thumbnail of Pathway Fractional Integral Operator on Some τ-extensions of Lauricella Functions of Several Variables

Journal of Mathematics and Informatics, 2021

In this paper, we establish new results as images of τ-extensions of Lauricella functions of seve... more In this paper, we establish new results as images of τ-extensions of Lauricella functions of several variables using the pathway fractional integral operator. The pathway fractional integral operator's motivation is a switching mechanism that transforms one fractional form to another with important applications. Some interesting special cases of our main findings are also highlighted.

Research paper thumbnail of Annals of A Reliable Treatment of Iterative Laplace Transform Method for Fractional Telegraph Equations

Abstract. In this paper a reliable algorithm for the iterative Laplace transform method (ILTM) is... more Abstract. In this paper a reliable algorithm for the iterative Laplace transform method (ILTM) is presented. ILTM is a combination of Laplace transform method and Iterative method to solve space- and time- fractional telegraph equations. The fractional derivatives are considered in Caputo sense. Closed form analytical expressions are derived in terms of the Mittag-Leffler functions. An illustrative numerical case study is presented for the proposed method to show the preciseness and effectiveness of the method.

Research paper thumbnail of A Reliable Treatment of Iterative Laplace Transform Method for Fractional Telegraph Equations

Abstract. In this paper a reliable algorithm for the iterative Laplace transform method (ILTM) is... more Abstract. In this paper a reliable algorithm for the iterative Laplace transform method (ILTM) is presented. ILTM is a combination of Laplace transform method and Iterative method to solve spaceand timefractional telegraph equations. The fractional derivatives are considered in Caputo sense. Closed form analytical expressions are derived in terms of the Mittag-Leffler functions. An illustrative numerical case study is presented for the proposed method to show the preciseness and effectiveness of the method.

Research paper thumbnail of Iterative Laplace Transform Method for Solving Fractional Heat and Wave- Like Equations

In this paper, we derive the closed form solutions of the fractional heat and wave like equations... more In this paper, we derive the closed form solutions of the fractional heat and wave like equations in terms of Mittag-Leffler functions by the use of iterative Laplace transform method. In the process the time-fractional derivatives are considered in Caputo sense for the said problem.

Research paper thumbnail of An efficient analytical approach for solving fractional Fokker-Planck equations

The present study focuses on investigating the approximate analytical solutions of linear and non... more The present study focuses on investigating the approximate analytical solutions of linear and nonlinear FokkerPlanck equations (FPEs) with spaceand time-fractional derivatives using an efficient analytical method, namely the Sumudu transform iterative method (STIM).The fractional derivatives are represented in the terms of Caputo. Analytical outcomes are obtained in the form of a converging series with easily computable components and are shown graphically. The results of the study suggest that the approach is simple to implement and very attractive in terms of computation.

Research paper thumbnail of An Efficient Computation Approach for Abel's Integral Equations of the Second Kind

This paper presents the application of a new powerful method named as q-homotopy analysis transfo... more This paper presents the application of a new powerful method named as q-homotopy analysis transform method (q-HATM). The q-HATM is a combination of the q-homotopy analysis scheme and the Laplace transform approach and more general than other existing techniques. Abel’s integral equation of the second kind has been solved by using this method. We solve some examples and plot the graphs. The numerical solutions are shown in the form of graphs.

Research paper thumbnail of • ANALYTICAL SOLUTION OF ABEL’S INTEGRAL EQUATION OF THE FIRST KIND BY USING q-HOMOTOPY ANALYSIS TRANSFORM METHOD

International Journal of Mathematical Archive EISSN 2229-5046, Jun 27, 2021

Research paper thumbnail of An Efficient Computation Approach for Abel’s Integral Equations of the Second Kind

This paper presents the application of a new powerful method named as q-homotopy analysis transfo... more This paper presents the application of a new powerful method named as q-homotopy analysis transform method (q-HATM). The q-HATM is a combination of the q-homotopy analysis scheme and the Laplace transform approach and more general than other existing techniques. Abel’s integral equation of the second kind has been solved by using this method. We solve some examples and plot the graphs. The numerical solutions are shown in the form of graphs.

Research paper thumbnail of Analytical Approach to Fractional Navier–Stokes Equations by Iterative Laplace Transform Method

Mathematical Modelling, Applied Analysis and Computation