$Fractional integro-differential equations with nonlocal conditions and ψ–Hilfer fractional derivative$

Fractional integro-differential equations with nonlocal conditions and ψ–Hilfer fractional derivative

Considering a fractional integro-differential equation with nonlocal conditions involving a general form of Hilfer fractional derivative with respect to another function. We show that weighted Cauchy-type problem is equivalent to a Volterra integral equation, we also prove the existence, uniquenes...

Full description

Bibliographic Details
Main Authors:	Mohammed S. Abdo, Satish K. Panchal, Hussien Shafei Hussien
Format:	Article
Language:	English
Published:	Vilnius Gediminas Technical University 2019-10-01
Series:	Mathematical Modelling and Analysis
Subjects:	fractional integro-diﬀerential equations ψ -Hilfer fractional derivative ψ-fractional integral existence and and Ulam-Hyers stability ﬁxed point theorem Mittag-Leﬄer function
Online Access:	https://journals.vgtu.lt/index.php/MMA/article/view/6330

id	doaj-cab68e5e3bb749cf9b5dac4293a0a349
record_format	Article
spelling	doaj-cab68e5e3bb749cf9b5dac4293a0a3492021-07-02T10:28:30ZengVilnius Gediminas Technical UniversityMathematical Modelling and Analysis1392-62921648-35102019-10-0124410.3846/mma.2019.034Fractional integro-differential equations with nonlocal conditions and ψ–Hilfer fractional derivativeMohammed S. Abdo0Satish K. Panchal1Hussien Shafei Hussien2Department of Mathematics, Dr. Babasaheb Ambedkar Marathwada University, Aurangabad, 431004 (M.S.), India; Department of Mathematics, Hodeidah University, Yemen, Drehemi road, P.O.Box 3114, 250416 Al-Hodeidah, YemenDepartment of Mathematics, Dr. Babasaheb Ambedkar Marathwada University, Aurangabad, 431004 (M.S.), IndiaDepartment of Mathematics, Faculty of science, South Valley University, 83523 Qena, Egypt Considering a fractional integro-differential equation with nonlocal conditions involving a general form of Hilfer fractional derivative with respect to another function. We show that weighted Cauchy-type problem is equivalent to a Volterra integral equation, we also prove the existence, uniqueness of solutions and Ulam-Hyers stability of this problem by employing a variety of tools of fractional calculus including Banach fixed point theorem and Krasnoselskii's fixed point theorem. An example is provided to illustrate our main results. https://journals.vgtu.lt/index.php/MMA/article/view/6330fractional integro-diﬀerential equationsψ -Hilfer fractional derivativeψ-fractional integralexistence and and Ulam-Hyers stabilityﬁxed point theoremMittag-Leﬄer function
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Mohammed S. Abdo Satish K. Panchal Hussien Shafei Hussien
spellingShingle	Mohammed S. Abdo Satish K. Panchal Hussien Shafei Hussien Fractional integro-differential equations with nonlocal conditions and ψ–Hilfer fractional derivative Mathematical Modelling and Analysis fractional integro-diﬀerential equations ψ -Hilfer fractional derivative ψ-fractional integral existence and and Ulam-Hyers stability ﬁxed point theorem Mittag-Leﬄer function
author_facet	Mohammed S. Abdo Satish K. Panchal Hussien Shafei Hussien
author_sort	Mohammed S. Abdo
title	Fractional integro-differential equations with nonlocal conditions and ψ–Hilfer fractional derivative
title_short	Fractional integro-differential equations with nonlocal conditions and ψ–Hilfer fractional derivative
title_full	Fractional integro-differential equations with nonlocal conditions and ψ–Hilfer fractional derivative
title_fullStr	Fractional integro-differential equations with nonlocal conditions and ψ–Hilfer fractional derivative
title_full_unstemmed	Fractional integro-differential equations with nonlocal conditions and ψ–Hilfer fractional derivative
title_sort	fractional integro-differential equations with nonlocal conditions and ψ–hilfer fractional derivative
publisher	Vilnius Gediminas Technical University
series	Mathematical Modelling and Analysis
issn	1392-6292 1648-3510
publishDate	2019-10-01
description	Considering a fractional integro-differential equation with nonlocal conditions involving a general form of Hilfer fractional derivative with respect to another function. We show that weighted Cauchy-type problem is equivalent to a Volterra integral equation, we also prove the existence, uniqueness of solutions and Ulam-Hyers stability of this problem by employing a variety of tools of fractional calculus including Banach fixed point theorem and Krasnoselskii's fixed point theorem. An example is provided to illustrate our main results.
topic	fractional integro-diﬀerential equations ψ -Hilfer fractional derivative ψ-fractional integral existence and and Ulam-Hyers stability ﬁxed point theorem Mittag-Leﬄer function
url	https://journals.vgtu.lt/index.php/MMA/article/view/6330
work_keys_str_mv	AT mohammedsabdo fractionalintegrodifferentialequationswithnonlocalconditionsandpshilferfractionalderivative AT satishkpanchal fractionalintegrodifferentialequationswithnonlocalconditionsandpshilferfractionalderivative AT hussienshafeihussien fractionalintegrodifferentialequationswithnonlocalconditionsandpshilferfractionalderivative
_version_	1721332045916930048

Fractional integro-differential equations with nonlocal conditions and ψ–Hilfer fractional derivative

Similar Items