scholarly journals p , q -Extended Struve Function: Fractional Integrations and Application to Fractional Kinetic Equations

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Haile Habenom ◽  
Abdi Oli ◽  
D. L. Suthar
Keyword(s):  
Applied Mathematics ◽  
Kinetic Equations ◽  
Integral Operators ◽  
Function Technique ◽  
Gauss Hypergeometric Function ◽  
Fractional Integral Operators ◽  
Special Cases ◽  
Generalized Fractional Integral ◽  
Fractional Kinetic Equations ◽  
Mathematics And Physics

In this paper, the generalized fractional integral operators involving Appell’s function F 3 ⋅ in the kernel due to Marichev–Saigo–Maeda are applied to the p , q -extended Struve function. The results are stated in terms of Hadamard product of the Fox–Wright function ψ r s z and the p , q -extended Gauss hypergeometric function. A few of the special cases (Saigo integral operators) of our key findings are also reported in the corollaries. In addition, the solutions of a generalized fractional kinetic equation employing the concept of Laplace transform are also obtained and examined as an implementation of the p , q -extended Struve function. Technique and findings can be implemented and applied to a number of similar fractional problems in applied mathematics and physics.

scholarly journals On Fractional Integral Inequalities Involving Hypergeometric Operators

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
D. Baleanu ◽  
S. D. Purohit ◽  
Praveen Agarwal
Keyword(s):  
Hypergeometric Function ◽  
Fractional Integral ◽  
Integral Operators ◽  
Integral Inequalities ◽  
Gauss Hypergeometric Function ◽  
Liouville Type ◽  
Fractional Integral Operators ◽  
Special Cases ◽  
Chebyshev Functional

Here we aim at establishing certain new fractional integral inequalities involving the Gauss hypergeometric function for synchronous functions which are related to the Chebyshev functional. Several special cases as fractional integral inequalities involving Saigo, Erdélyi-Kober, and Riemann-Liouville type fractional integral operators are presented in the concluding section. Further, we also consider their relevance with other related known results.

scholarly journals Some new inequalities for generalized convex functions pertaining generalized fractional integral operators and their applications

2021 ◽  
Vol 17 (1) ◽  
pp. 37-64
Author(s):  
A. Kashuri ◽  
M.A. Ali ◽  
M. Abbas ◽  
M. Toseef
Keyword(s):  
Differentiable Function ◽  
Convex Functions ◽  
Fractional Integral ◽  
Integral Operators ◽  
Generalized Convex Functions ◽  
Fractional Integral Operators ◽  
Special Cases ◽  
Generalized Fractional Integral ◽  
Generalized Fractional Integral Operators ◽  
New Inequalities

Abstract In this paper, authors establish a new identity for a differentiable function using generic integral operators. By applying it, some new integral inequalities of trapezium, Ostrowski and Simpson type are obtained. Moreover, several special cases have been studied in detail. Finally, many useful applications have been found.

scholarly journals Generalized Fractional Integral Operators Pertaining to the Product of Srivastava’s Polynomials and Generalized Mathieu Series

Mathematics ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 206 ◽  
Author(s):  
K.S. Nisar ◽  
D.L. Suthar ◽  
M. Bohra ◽  
S.D. Purohit
Keyword(s):  
Hypergeometric Function ◽  
Fractional Integral ◽  
Special Functions ◽  
Integral Operators ◽  
Factor X ◽  
Fractional Integral Operators ◽  
Special Cases ◽  
Generalized Fractional Integral ◽  
Mathieu Series ◽  
Srivastava’S Polynomials

Fractional calculus image formulas involving various special functions are important for evaluation of generalized integrals and to obtain the solution of differential and integral equations. In this paper, the Saigo’s fractional integral operators involving hypergeometric function in the kernel are applied to the product of Srivastava’s polynomials and the generalized Mathieu series, containing the factor x λ ( x k + c k ) − ρ in its argument. The results are expressed in terms of the generalized hypergeometric function and Hadamard product of the generalized Mathieu series. Corresponding special cases related to the Riemann–Liouville and Erdélyi–Kober fractional integral operators are also considered.

scholarly journals Integral inequalities via Raina’s fractional integrals operator with respect to a monotone function

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Shu-Bo Chen ◽  
Saima Rashid ◽  
Zakia Hammouch ◽  
Muhammad Aslam Noor ◽  
Rehana Ashraf ◽  
...  
Keyword(s):  
Fractional Integral ◽  
Monotone Function ◽  
Integral Operators ◽  
Integral Inequalities ◽  
Fractional Integrals ◽  
Liouville Type ◽  
Fractional Integral Operators ◽  
Special Cases ◽  
Generalized Fractional Integral

AbstractWe establish certain new fractional integral inequalities involving the Raina function for monotonicity of functions that are used with some traditional and forthright inequalities. Taking into consideration the generalized fractional integral with respect to a monotone function, we derive the Grüss and certain other associated variants by using well-known integral inequalities such as Young, Lah–Ribarič, and Jensen integral inequalities. In the concluding section, we present several special cases of fractional integral inequalities involving generalized Riemann–Liouville, k-fractional, Hadamard fractional, Katugampola fractional, $(k,s)$ ( k , s ) -fractional, and Riemann–Liouville-type fractional integral operators. Moreover, we also propose their pertinence with other related known outcomes.

scholarly journals New General Variants of Chebyshev Type Inequalities via Generalized Fractional Integral Operators

Mathematics ◽  
2021 ◽  
Vol 9 (2) ◽  
pp. 122
Author(s):  
Ahmet Ocak Akdemir ◽  
Saad Ihsan Butt ◽  
Muhammad Nadeem ◽  
Maria Alessandra Ragusa
Keyword(s):  
Fractional Integral ◽  
Integral Operators ◽  
Chebyshev Inequality ◽  
Fractional Integral Operators ◽  
Integrable Functions ◽  
Inequality Theory ◽  
Special Cases ◽  
Generalized Fractional Integral ◽  
Chebyshev's Inequality ◽  
Generalized Fractional Integral Operators

In this study, new and general variants have been obtained on Chebyshev’s inequality, which is quite old in inequality theory but also a useful and effective type of inequality. The main findings obtained by using integrable functions and generalized fractional integral operators have generalized many existing results as well as iterating the Chebyshev inequality in special cases.

scholarly journals A Study on Generalized Multivariable Mittag-Leffler Function via Generalized Fractional Calculus Operators

2019 ◽  
Vol 2019 ◽  
pp. 1-7 ◽  
Author(s):  
D. L. Suthar ◽  
Mitku Andualem ◽  
Belete Debalkie
Keyword(s):  
Integral Operators ◽  
Fractional Integrals ◽  
Fractional Integral Operators ◽  
Generalized Fractional Calculus ◽  
Special Cases ◽  
Fractional Calculus Operators ◽  
Generalized Fractional Integral ◽  
Generalized Fractional Calculus Operators ◽  
Fox’S H Function ◽  
Generalized Fractional Integral Operators

We study some properties of generalized multivariable Mittag-Leffler function. Also we establish two theorems, which give the images of this function under the generalized fractional integral operators involving Fox’s H-function as kernel. Relating affirmations in terms of Saigo, Erdélyi-Kober, Riemann-Liouville, and Weyl type of fractional integrals are also presented. Some known special cases have also been mentioned in the concluding section.

scholarly journals Generalized Fractional Integral Operators andM-Series

2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
A. M. Khan ◽  
R. K. Kumbhat ◽  
Amit Chouhan ◽  
Anita Alaria
Keyword(s):  
Hypergeometric Function ◽  
Numerical Computation ◽  
Power Function ◽  
Fractional Integral ◽  
Integral Operators ◽  
Generalized Hypergeometric Function ◽  
Fractional Integral Operators ◽  
Special Cases ◽  
Generalized Fractional Integral ◽  
Generalized Fractional Integral Operators

Two fractional integral operators associated with FoxH-function due to Saxena and Kumbhat are applied toM-series, which is an extension of both Mittag-Leffler function and generalized hypergeometric functionpFq. The Mellin and Whittaker transforms are obtained for these compositional operators withM-series. Further some interesting properties have been established including power function and Riemann-Liouville fractional integral operators. The results are expressed in terms ofH-function, which are in compact form suitable for numerical computation. Special cases of the results are also pointed out in the form of lemmas and corollaries.

scholarly journals Pathway fractional integral operators of generalized k-wright function and k4-function

2017 ◽  
Vol 35 (2) ◽  
pp. 235 ◽  
Author(s):  
Dinesh Kumar ◽  
Ram Kishore Saxena ◽  
Jitendra Daiya
Keyword(s):  
Fractional Integral ◽  
Fractional Integration ◽  
Integral Operators ◽  
Wright Function ◽  
Finite Product ◽  
Fractional Integral Operators ◽  
Integral Formulas ◽  
Fractional Integration Operator ◽  
Composition Formula ◽  
Special Cases

In the present work we introduce a composition formula of the pathway fractional integration operator with finite product of generalized K-Wright function and K4-function. The obtained results are in terms of generalized Wright function.Certain special cases of the main results given here are also considered to correspond with some known and new (presumably) pathway fractional integral formulas.

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