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OALib Journal期刊

ISSN: 2333-9721

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An Introduction to the Generalized Fractional Integration
Kishan Sharma
Boletim da Sociedade Paranaense de Matemática , 2012,
Abstract: The purpose of the present paper is to investigate the generalizedfractional integration of the generalized M-series.Some results derived by Saxena and Saigo [13], Samko, Kilbas and Marichev [15] are the special cases of the main results derived in this paper.
Generalized fractional integration of the overline{H}-function
Praveen Agarwal
Le Matematiche , 2012,
Abstract: A significantly large number of earlier works on the subject of fractional calculus give interesting account of the theory and applications of fractional calculus operators in many different areas of mathematical analysis (such as ordinary and partial differential equations, integral equations, special functions, summation of series, et cetera). In the present paper, we study and develop the generalized fractional integral operators given by Saigo. First, we establish two Theorems that give the images of the product of H-function and a general class of polynomials in Saigo operators. On account of the general nature of the Saigo operators, H-function and a general class of polynomials a large number of new and known Images involving Riemann-Liouville and Erdélyi-Kober fractional integral operators and several special functions notably generalized Wright hypergeometric function, generalized Wright-Bessel function, the polylogarithm and Mittag-Leffler functions follow as special cases of our main findings.
On certain operational formulae for multivariable basic hypergeometric functions
S. D. Purohit and R. K. Raina
ACTA MATHEMATICA UNIVERSITATIS COMENIANAE , 2009,
Abstract: In the present paper certain operational formulae involving Riemann-Liouville and Kober fractional q-integral operators for an analytic function are derived. The usefulness of the main results are exhibited by considering some examples which also yield q-extensions of some known results for ordinary hypergeometric functions of one and more variables.
On certain operational formulae for multivariable basic hypergeometric functions
S. D. Purohit,R. K. Raina
ACTA MATHEMATICA UNIVERSITATIS COMENIANAE , 2009,
Abstract: In the present paper certain operational formulae involving Riemann-Liouville and Kober fractional q-integral operators for an analytic function are derived. The usefulness of the main results are exhibited by considering some examples which also yield q-extensions of some known results for ordinary hypergeometric functions of one and more variables.
On certain subclasses of p-valent functions defined in terms of certain fractional derivative operators
Nahar, T. S.,Raina, R. K.
- , 2002,
Abstract: Sa？etak In the present paper we study certain subclasses Hλ,μ,η(a,b,pσ) and Kλ,μ,η(a,b,pσ) of analytic and p-valent functions. The results presented include coefficient estimates and distorsion properties for functions belonging to such classes. Further results giving closure theorems, various properties and modified Hadamard products of several functions belonging to above classes are also mentioned
ON TURáN'S TYPE INEQUALITIES FOR SOME SPECIAL FUNCTIONS AND OPERATORS
Proyecciones (Antofagasta) , 2010, DOI: 10.4067/S0716-09172010000200002
Abstract: the purpose of this paper is to use the generalized schwarz inequality to give a short proofs of new turán-type inequalities for some special functions and operators.
ON TURáN'S TYPE INEQUALITIES FOR SOME SPECIAL FUNCTIONS AND OPERATORS
Hari Singh Parihar
Proyecciones (Antofagasta) , 2010,
Abstract: The purpose of this paper is to use the generalized Schwarz inequality to give a short proofs of new Turán-type inequalities for some special functions and operators.
On the Approximate Solution of Fractional Logistic Differential Equation Using Operational Matrices of Bernstein Polynomials  [PDF]
R. F. Al-Bar
Applied Mathematics (AM) , 2015, DOI: 10.4236/am.2015.612184
Abstract: In this paper, operational matrices of Bernstein polynomials (BPs) are presented for solving the non-linear fractional Logistic differential equation (FLDE). The fractional derivative is described in the Riemann-Liouville sense. The operational matrices for the fractional integration in the Riemann-Liouville sense and the product are used to reduce FLDE to the solution of non-linear system of algebraic equations using Newton iteration method. Numerical results are introduced to satisfy the accuracy and the applicability of the proposed method.
Existence of deviating fractional differential equation
Ibrahim,Rabha W;
Cubo (Temuco) , 2012, DOI: 10.4067/S0719-06462012000300009
Abstract: in this paper we shall establish sufficient conditions for the existence of solutions of a class of fractional differential equation (cauchy type ) and its solvability in a subset of the banach space. the main tool used in our study is the non-expansive operator technique. the non integer case is taken in sense of riemann liouville fractional operators. applications are illustrated.
Existence of deviating fractional differential equation
Rabha W Ibrahim
Cubo : A Mathematical Journal , 2012,
Abstract: In this paper we shall establish sufficient conditions for the existence of solutions of a class of fractional differential equation (Cauchy type ) and its solvability in a subset of the Banach space. The main tool used in our study is the non-expansive operator technique. The non integer case is taken in sense of Riemann Liouville fractional operators. Applications are illustrated. En este artículo establecemos condiciones suficientes para la existencia de soluciones de una clase de ecuaciones diferenciales fraccionales (del tipo Cauchy) y su solubilidad en un subconjunto de un espacio de Banach. La principal herramienta utilizada en nuestro estudio es la técnica del operador no expansivo. El caso no entero se escoge en el sentido de operadores fraccionales Riemann-Liouville. Además, se ilustran aplicaciones.
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