A novel study on nonlinear fractional differential equations: general solution

Subject Areas : Mathematical Engineering

Mousa Ilie ¹ , Ali Khoshkenar ²

1 - Department of Mathematics, Rasht Branch, Islamic Azad University, Rasht, Iran
2 - Department of Mathematics, Rasht Branch, Islamic Azad University, Rasht, Iran

Received: 2022-12-30 Accepted : 2023-06-09 Published : 2022-12-01

Keywords: Truncated M-fractional derivative, Local M-fractional integral, Abel' s technique, M-fractional Bernoulli equation, M-fractional Riccati equation,

Abstract :

In the present article, the Abel's technique has been developed to finding a general solution of the modified linear first-order ordinary differential equations in the sense of the truncated M-fractional derivative. By using proposed approach, a general solution of two well-recognized nonlinear first-order ordinary differential equations, Bernoulli and Riccati, in agreement with truncated M-fractional derivative have been obtained. For each equation, some examples are presented for satisfactory and efficiency of the proposed method.

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