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

Mohammed S. Abdo & Satish K. Panchal

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.

  • AMS Subject Headings

34K37 26A33 34A12 47H10

  • Copyright

COPYRIGHT: © Global Science Press

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