TY - JOUR
T1 - Fractional Integro-Differential Equations Involving $\psi$-Hilfer Fractional Derivative
AU - Abdo , Mohammed S.
AU - Panchal , Satish K.
JO - Advances in Applied Mathematics and Mechanics
VL - 2
SP - 338
EP - 359
PY - 2019
DA - 2019/01
SN - 11
DO - http://doi.org/10.4208/aamm.OA-2018-0143
UR - https://global-sci.org/intro/article_detail/aamm/12966.html
KW - Fractional integro-differential equations, $\psi$-Hilfer fractional derivative and
$\psi$-fractional integral, existence, uniqueness and Ulam-Hyers stability, fixed point theorem.
AB - <p style="text-align: justify;">Considering a fractional integro-differential equation 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. An example is provided to illustrate our main results.</p>