On the solutions of implicit arbitrary orders differential equations in Banach spaces | ||
| Journal of Fractional Calculus and Applications | ||
| Volume 14, Issue 2, July 2023, Pages 1-7 PDF (382.05 K) | ||
| Document Type: Regular research papers | ||
| DOI: 10.21608/jfca.2023.203195.1006 | ||
| Author | ||
| Aziza A.H Elhassy* | ||
| Department of mathematics, faculty of science,University of Derna, Derna, Libya | ||
| Abstract | ||
| The fixed point theorem by Arino-Gautier and Penot is used and we depend on converting of the mentioned equations to the form of functional integral equations to establish existence of pseudo-solutions to a Cauchy problem of differential equation of arbitrary orders in Banach spaces. The topic of fractional calculus ( derivatives and integrals of arbitrary orders) is enjoying growing interest not only in Mathematics, but also in Physics, Engineering and Mathematical Biology. The very rst approach via weak topology follows by Szep. Then more ideas are taken from from papers by Kubiaczyk, Szufla or Kubiaczyk . the existence of weak solutions for the initial value problem of the arbitrary (fractional) orders differential equation in the reflexive Banach space E have been considered, for the fi rst time, by Salem and El-Sayed. Let E be a Banach space with norm k : k and dual . Moreover, let Ew denote the space E with its weak topology. By C = C[I;E] the Banach space of strongly continuous functions x with jjxjjC = sup jjx(t)jjE; t in I | ||
| Keywords | ||
| Fractional differential equation; fractional Pettis integral; Pseudo solution; fixed point | ||
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