New Fractional Operators Including Wright Function in Their Kernels

Abstract

In this paper, we defined new two-fractional derivative operators with a Wright function in their kernels. We also gave their Laplace and inverse Laplace transforms. Then, we presented some connections between the new fractional operators. Furthermore, as examples, we obtained solutions of differential equations involving new fractional operators. Finally, we examined the relations of the new fractional operators with the fractional operators, which can be found in the literature.

Keywords

• Wright function
• Laplace transform
• fractional derivatives
• fractional differential equations

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