Browsing by Author "Agarwal, P."

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Citation - WoS: 19
Citation - Scopus: 20
Approximating System of Ordinary Differential-Algebraic Equations Via Derivative of Legendre Polynomials Operational Matrices
(World Scientific Publ Co Pte Ltd, 2023) Abdelhakem, M.; Baleanu, D.; Agarwal, P.; Moussa, Hanaa; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
Legendre polynomials' first derivatives have been used as the basis function via the pseudo-Galerkin spectral method. Operational matrices for derivatives have been used and extended to deal with the system of ordinary differential-algebraic equations. An algorithm via those matrices has been designed. The accuracy and efficiency of the proposed algorithm had been shown by two techniques, theoretically, via the boundedness of the approximated expansion and numerically through numerical examples.
Citation - WoS: 8
Citation - Scopus: 9
Certain Fractional Integral Formulas Involving the Product of Generalized Bessel Functions
(Hindawi Ltd, 2013) Agarwal, P.; Purohit, S. D.; Baleanu, D.; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
We apply generalized operators of fractional integration involving Appell's function F-3(.) due to Marichev-Saigo-Maeda, to the product of the generalized Bessel function of the first kind due to Baricz. The results are expressed in terms of the multivariable generalized Lauricella functions. Corresponding assertions in terms of Saigo, Erdelyi-Kober, Riemann-Liouville, and Weyl type of fractional integrals are also presented. Some interesting special cases of our two main results are presented. We also point out that the results presented here, being of general character, are easily reducible to yield many diverse new and known integral formulas involving simpler functions.
Citation - WoS: 41
Citation - Scopus: 50
A Novel Jacobi Operational Matrix for Numerical Solution of Multi-Term Variable-Order Fractional Differential Equations
(Taylor & Francis Ltd, 2020) Baleanu, D.; Agarwal, P.; El-Sayed, A. A.; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In this article, we introduce a numerical technique for solving a class of multi-term variable-order fractional differential equation.The method depends on establishing a shifted Jacobi operational matrix (SJOM) of fractional variable-order derivatives. By using the constructed (SJOM) in combination with the collocation technique, the main problem is reduced to an algebraic system of equations that can be solved numerically. The bound of the error estimate for the suggested method is investigated. Numerical examples are introduced to illustrate the applicability, generality, and accuracy of the proposed technique. Moreover, many physical applications problems that have the multi-term variable-order fractional differential equation formulae such as the damped mechanical oscillator problem and Bagley-Torvik equation can be solved via the presented method. Furthermore, the proposed method will be considered as a generalization of many numerical techniques.
Citation - WoS: 40
Citation - Scopus: 56
On the Solutions of Certain Fractional Kinetic Equations Involving K-Mittag Function
(Springer, 2018) Chand, M.; Baleanu, D.; O'Regan, D.; Jain, Shilpi; Agarwal, P.; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
The aim of the present paper is to develop a new generalized form of the fractional kinetic equation involving a generalized k-Mittag-Leffler function E-k,zeta,eta(gamma,rho)(center dot). The solutions of fractional kinetic equations are discussed in terms of the Mittag-Leffler function. Further, numerical values of the results and their graphical interpretation is interpreted to study the behavior of these solutions. The results established here are quite general in nature and capable of yielding both known and new results.