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21 results on '"CHINCHANE, VAIJANATH L."'

1. Some Minkowski-type inequalities using generalized proportional Hadamard fractional integral operators

Author

Nale, Asha B., Panchal, Satish K., and Chinchane, Vaijanath L.

Subjects
Mathematics - General Mathematics, 26D10, 26A33, 05A30, 26D53
Abstract

The main objective of present investigation to obtain some Minkowski-type fractional integral inequalities using generalised proportional Hadamard fractional integral operators which is introduced by Rahman et al in the paper (certain inequalities via generalized proportional Hadamard fractional integral operators), Advances in Differential Equations, (2019), 2019:454. In addition, we establish some other fractional integral inequalities for positive and continuous functions.

Published
2020

2. Grüss-type fractional inequality via Caputo-Fabrizio integral operator

Author

Nale Asha B., Panchal Satish K., and Chinchane Vaijanath L.

Subjects
grüss-type inequality, caputo-fabrizio fractional integral and integral inequality, 26d10, 26d33, Mathematics, QA1-939
Abstract

In this article, the main objective is to establish the Grüss-type fractional integral inequalities by employing the Caputo-Fabrizio fractional integral.

Published
2022
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3. Note on fractional integral inequality involving convex functions using Saigo fractional integral

Author

Chinchane, Vaijanath L. and Pachpatte, Deepak B.

Subjects
Mathematics - Classical Analysis and ODEs, 26D10, 26A33
Abstract

The aim of the present paper is to obtain some new fractional integral inequalities for convex functions. Saigo fractional integral operator is used to establish the results., Comment: The paper is withdraw due to several of grammatical misprints throughout the paper. the references are inconsistently written and want to write some corollaries which is special case of saigo operators (i.e Erdeyi-Kober fractional operators)

Published
2017

5. P$\acute{o}$lya-Szeg$\ddot{o}$ fractional inequality via Hadamard fractional integral

Author

Chinchane, Vaijanath L., Pachpatte, Deepak B., and Nale, Asha B.

Subjects
Mathematics - Classical Analysis and ODEs, 26D10, 26A33
Abstract

In the present paper, we establish some new fractional integral inequalities similar to P$\acute{o}$lya-Szeg$\ddot{o}$ integral inequality and fractional inequality related to Minkowsky inequality by using the Hadamard fractional integral operator. Also, we discuss few spacial cases of these inequalities., Comment: 11 pages

Published
2016

7. Study of Uniqueness and Ulam-Type Stability of Abstract Hadamard Fractional Differential Equations of Sobolev Type via Resolvent Operators.

Author

Ould Melha, Khellaf, Mohammed Djaouti, Abdelhamid, Latif, Muhammad Amer, and Chinchane, Vaijanath L.

Subjects
RESOLVENTS (Mathematics), PARTIAL differential equations
Abstract

This paper focuses on studying the uniqueness of the mild solution for an abstract fractional differential equation. We use Banach's fixed point theorem to prove this uniqueness. Additionally, we examine the stability properties of the equation using Ulam's stability. To analyze these properties, we consider the involvement of Hadamard fractional derivatives. Throughout this study, we put significant emphasis on the role and properties of resolvent operators. Furthermore, we investigate Ulam-type stability by providing examples of partial fractional differential equations that incorporate Hadamard derivatives. [ABSTRACT FROM AUTHOR]

Published
2024
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8. ABSTRACT FRACTIONAL DIFFERENTIAL EQUATIONS WITH CAPUTO--FABRIZIO DERIVATIVE.

Author

MELHA, KHELLAF OULD, DJILALI, MEDJAHED, and CHINCHANE, VAIJANATH L.

Subjects
FRACTIONAL differential equations, MATHEMATICS theorems, INTEGRAL inequalities, MATHEMATICAL inequalities, NONLINEAR operators
Abstract

The main objective of this paper is to prove the existence and uniqueness of mild solution for abstract differential equations by using the resolvent operators and fixed point theorem. Moreover, we studied some examples on partial differential equation with Caputo-Fabrizio derivative. [ABSTRACT FROM AUTHOR]

Published
2023
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12. A NOTE ON FRACTIONAL INEQUALITIES INVOLVING GENERALIZED KATUGAMPOLA FRACTIONAL INTEGRAL OPERATOR.

Author

NALE, ASHA B., PANCHAL, SATISH K., and CHINCHANE, VAIJANATH L.

Subjects
FRACTIONAL calculus, VARIATIONAL inequalities (Mathematics), INTEGRAL operators, CHEBYSHEV systems, SET theory
Abstract

The aim of this paper is to obtain some new fractional inequalities involving generalized Katugampola fractional integral operator by considering the extended Chebyshev functional in case of synchronous function. Also we obtain some fractional inequalities involving generalized Katugampola fractional integral. [ABSTRACT FROM AUTHOR]

Published
2023

15. ON WEIGHTED FRACTIONAL INEQUALITIES USING HADAMARD FRACTIONAL INTEGRAL OPERATOR.

Author

Nale, Asha B., Panchal, Satish K., and Chinchane, Vaijanath L.

Subjects
INTEGRAL operators, FRACTIONAL integrals, INTEGRAL inequalities, CONTINUOUS functions
Abstract

In this paper, firstly we introduced the Hadamard fractional integral operator whose kernel is of log( x/ t ) instead of the form of (x-t) which is involves both in the Riemann-Liouville and Caputo integral. In view of these, we obtain some new weighted fractional integral inequalities for positive and continuous function by employing Hadamard fractional integral operator. [ABSTRACT FROM AUTHOR]

Published
2021

16. New Approach to Minkowski Fractional Inequalities Using Generalized K-fractional Integral Operator

Author

Chinchane, Vaijanath L.; Department of Mathematics, Deogiri Institute of Engineering and Management Studies, Aurangabad - 431005 and Chinchane, Vaijanath L.; Department of Mathematics, Deogiri Institute of Engineering and Management Studies, Aurangabad - 431005

Abstract

In this paper, we obtain results related to Minkowski fractional integral inequality using generalized k-fractional integral operator is in terms of the Gauss hypergeometric function.

Published
2018

21. CERTAIN INEQUALITIES USING SAIGO FRACTIONAL INTEGRAL OPERATOR.

Author

Chinchane, Vaijanath L. and Pachpatte, Deepak B.

Subjects
*FRACTIONAL integrals, *CHEBYSHEV approximation, *MATHEMATICAL analysis, *INTEGRAL operators, *RIEMANN-Hilbert problems
Abstract

The main objective of this paper is to establish some new results on fractional integral inequalities by considering the extended Chebyshev functional in the case of synchronous function. The result is concerned with some inequalities using one fractional parameter and two parameters. [ABSTRACT FROM AUTHOR]

Published
2014

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