On a New Generalized Integral Operator and Certain Operating Properties

In this paper, we present a general definition of a generalized integral operator which contains as particular cases, many of the well-known, fractional and integer order integrals.

[1]  Shin Min Kang,et al.  Generalized Riemann-Liouville $k$ -Fractional Integrals Associated With Ostrowski Type Inequalities and Error Bounds of Hadamard Inequalities , 2018, IEEE Access.

[2]  Alqahtani,et al.  A Solution for Volterra Fractional Integral Equations by Hybrid Contractions , 2019, Mathematics.

[3]  G. Mittag-Leffler,et al.  Sur la représentation analytique d’une branche uniforme d’une fonction monogène , 1901 .

[4]  E. Karapınar,et al.  Large Contractions on Quasi-Metric Spaces with an Application to Nonlinear Fractional Differential Equations , 2019, Mathematics.

[5]  D. Baleanu,et al.  On Fractional Operators and Their Classifications , 2019, Mathematics.

[6]  Udita N. Katugampola New approach to a generalized fractional integral , 2010, Appl. Math. Comput..

[7]  A. Kilbas,et al.  On Mittag-Leffler type function and applications , 1998 .

[8]  E. Karapınar,et al.  Applying new fixed point theorems on fractional and ordinary differential equations , 2019, Advances in Difference Equations.

[9]  Sergei V. Rogosin,et al.  On the generalized mittag-leffler type functions , 1998 .

[10]  Juan E. Nápoles Valdés,et al.  New Hermite-Hadamard Type Inequalities Involving Non-Conformable Integral Operators , 2019, Symmetry.

[11]  Erdal Karapinar,et al.  Solutions of the Nonlinear Integral Equation and Fractional Differential Equation Using the Technique of a Fixed Point with a Numerical Experiment in Extended b-Metric Space , 2019, Symmetry.

[12]  G. Farid Study of a generalized Riemann-Liouville fractional integral via convex functions , 2020 .

[13]  A. Wiman Über den Fundamentalsatz in der Teorie der FunktionenEa(x) , 1905 .

[14]  M. Sababheh,et al.  A new definition of fractional derivative , 2014, J. Comput. Appl. Math..

[15]  J. A. Méndez-Bermúdez,et al.  On fractional Liénard--type systems , 2019, Revista Mexicana de Física.

[17]  F. Periago,et al.  Distributional fractional powers of the Laplacean. Riesz potentials , 1999 .

[18]  J. Machado,et al.  A Review of Definitions for Fractional Derivatives and Integral , 2014 .

[19]  F. Mainardi,et al.  Recent history of fractional calculus , 2011 .

[20]  Baleanu Dumitru Comments on: “The failure of certain fractional calculus operators in two physical models” by M. Ortigueira, V. Martynyuk, M. Fedula and J.A.T. Machado , 2020 .

[21]  Existence of solutions of generalized fractional differential equation with nonlocal initial condition , 2018, Mathematica Bohemica.

[22]  Megumi Saigo,et al.  On mittag-leffler type function, fractional calculas operators and solutions of integral equations , 1996 .