@article{Shehata_2024, title={Linear α −Differential Equations}, volume={5}, url={https://www.sabapub.com/index.php/jfcns/article/view/1118}, DOI={10.48185/jfcns.v5i1.1118}, abstractNote={<p>y α −differential equations, we mean that the branch studies differential equations containing fractional or real order derivatives. In [1], Shehata has overcome the problem of multiple previous definitions of<br />fractional calculus by putting an accurate definition of the α− fractional calculus using the normal way. He<br />concluded from this definition that the α fractional calculus is a complex-valued function that depends on<br />the principal root of the real number. As an extension of the study of fractional calculus and its importance<br />in applications, in this paper, we study differential equations that contain fractional differentials based on the<br />Shehata definition. We define and study the so-called linear α− differential equations of the first extension,<br />higher extension, and system of the first extension. We give the closed formula for each case. To illustrate our<br />result, we give some numerical examples of fractional differential equations and their solutions.</p>}, number={1}, journal={Journal of Fractional Calculus and Nonlinear Systems}, author={Shehata, Mohammed}, year={2024}, month={Jun.}, pages={12–31} }