Volume 11, Issue 2
Fractional Integro-Differential Equations Involving $\psi$-Hilfer Fractional Derivative

Adv. Appl. Math. Mech., 11 (2019), pp. 338-359.

Published online: 2019-01

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• Abstract

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.

• Keywords

Fractional integro-differential equations, $\psi$-Hilfer fractional derivative and $\psi$-fractional integral, existence, uniqueness and Ulam-Hyers stability, fixed point theorem.

34K37, 26A33, 34A12, 47H10

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@Article{AAMM-11-338, author = {Abdo , Mohammed S. and Panchal , Satish K.}, title = {Fractional Integro-Differential Equations Involving $\psi$-Hilfer Fractional Derivative}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2019}, volume = {11}, number = {2}, pages = {338--359}, abstract = {

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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2018-0143}, url = {http://global-sci.org/intro/article_detail/aamm/12966.html} }
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 -

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.

Mohammed S. Abdo & Satish K. Panchal. (2020). Fractional Integro-Differential Equations Involving $\psi$-Hilfer Fractional Derivative. Advances in Applied Mathematics and Mechanics. 11 (2). 338-359. doi:10.4208/aamm.OA-2018-0143
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