Fractional order differential and integral equations with Erdélyi-Kober operators: Explicit solutions by means of the transmutation method

2011 ◽  
Author(s):  
Virginia S. Kiryakova ◽  
George Venkov ◽  
Ralitza Kovacheva ◽  
Vesela Pasheva
Keyword(s):  
Integral Equations ◽  
Fractional Order ◽  
Explicit Solutions ◽  
Differential And Integral Equations

Overconvergence of series in generalized mittag-leffler functions

2017 ◽  
Vol 20 (2) ◽  
Author(s):  
Jordanka Paneva-Konovska
Keyword(s):  
Integral Equations ◽  
Fractional Order ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Necessary And Sufficient ◽  
Differential And Integral Equations

AbstractSeries defined by means of the three-parametric Mittag-Leffler functions, called also the Prabhakar functions, are considered in this paper. Their behaviour is investigated on the boundaries of the convergence domains. Necessary and sufficient conditions for their overconvergence are proposed. The corresponding results for series in Mittag-Leffler functions are discussed as a particular case. Such kind of results are motivated by the fact that the solutions of some fractional order differential and integral equations can be written in terms of series (or series of integrals) of Mittag-Leffler type functions.

scholarly journals ON BIVARIATE RETARDED INTEGRAL INEQUALITIES AND THEIR APPLICATIONS

2019 ◽  
pp. 553
Author(s):  
Fuat Usta ◽  
Mehmet Zeki Sarıkaya
Keyword(s):  
Differential Equations ◽  
Integral Equations ◽  
Fractional Order ◽  
Time Delays ◽  
Integral Inequalities ◽  
Partial Differential ◽  
Independent Variables ◽  
Fractional Order Differential Equations ◽  
Two Independent Variables ◽  
Differential And Integral Equations

In this paper, we obtain some retarded integral inequalities in two independent variables which can be used as tools in the theory of partial differential and integral equations with time delays. The presented inequalities are of new forms compared with the existing ones so far in the literature. In order to illustrate the validity of the theorems we give one application for them for the solution to certain fractional order differential equations.

Existence, uniqueness and limit property of solutions to quadratic Erdélyi-Kober type integral equations of fractional order

Open Physics ◽  
2013 ◽  
Vol 11 (6) ◽  
Author(s):  
JinRong Wang ◽  
Chun Zhu ◽  
Michal Fečkan
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Integral Equations ◽  
Fractional Order ◽  
Point Theorem ◽  
Measure Of Noncompactness ◽  
Existence Results ◽  
Limit Property ◽  
Type Integral

AbstractIn this paper, we apply certain measure of noncompactness and fixed point theorem of Darbo type to derive the existence and limit property of solutions to quadratic Erdélyi-Kober type integral equations of fractional order with three parameters. Moreover, we also present the uniqueness and another existence results of the solutions to the above equations. Finally, two examples are given to illustrate the obtained results.

scholarly journals Asymptotic behavior of fractional order Riemann-Liouville Volterra-Stieltjes integral equations

2015 ◽  
Vol 27 (3) ◽  
pp. 311-323
Author(s):  
Saïd Abbas ◽  
Mouffak Benchohra ◽  
Boualem A. Slimani ◽  
Juan J. Trujillo
Keyword(s):  
Asymptotic Behavior ◽  
Integral Equations ◽  
Fractional Order ◽  
Stieltjes Integral

scholarly journals Qualitative Theory of Functional Differential and Integral Equations 2016

2017 ◽  
Vol 2017 ◽  
pp. 1-2
Author(s):  
Cemil Tunç ◽  
Bingwen Liu ◽  
Luís R. Sanchez ◽  
Mohsen Alimohammady ◽  
Octavian G. Mustafa ◽  
...  
Keyword(s):  
Integral Equations ◽  
Qualitative Theory ◽  
Functional Differential ◽  
Differential And Integral Equations
Sign in / Sign up

Export Citation Format

Share Document