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  • 1.
    Mursaleen, Mohammad
    et al.
    Aligarh Muslim University, India.
    Pourhadi, Ehsan
    Linnaeus University, Faculty of Technology, Department of Mathematics. Iran University of Science and Technology, Iran.
    Saadati, Reza
    Iran University of Science and Technology, Iran.
    Solvability of infinite systems of second-order differential equations with boundary conditions in lp: Solvability of infinite systems2019In: Quaestiones Mathematicae. Journal of the South African Mathematical Society, ISSN 1607-3606, E-ISSN 1727-933X, p. 1-20Article in journal (Refereed)
    Abstract [en]

    In this paper, governed by the fundamental solutions we introduce the Green’s function of the second-order differential equations in general form with respect to boundary conditions and deal with the solvability of the infinite system of a second-order differential equations. Using the ideas of Hausdorff measure of noncompactness and Meir-Keleer condensing operator we seek the sufficient conditions to justify the existence of solutions for the aforementioned system in the Banach sequence space lp

  • 2.
    Pourhadi, Ehsan
    et al.
    Linnaeus University, Faculty of Technology, Department of Mathematics. Iran University of Science and Technology, Iran.
    Khrennikov, Andrei
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    On the solutions of Cauchy problem for two classes of semi-linear pseudo-differential equations over p-adic field2018In: P-Adic Numbers, Ultrametric Analysis, and Applications, ISSN 2070-0466, E-ISSN 2070-0474, Vol. 10, no 4, p. 322-343Article in journal (Refereed)
    Abstract [en]

    Throughout this paper, using the p-adic wavelet basis together with the help of separation of variables and the Adomian decomposition method (as a scheme in numerical analysis) we initially investigate the solution of Cauchy problem for two classes of the first and second order of pseudo-differential equations involving the pseudo-differential operators such as Taibleson fractional operator in the setting of p-adic field.

  • 3.
    Pourhadi, Ehsan
    et al.
    Linnaeus University, Faculty of Technology, Department of Mathematics. Iran University of Science and Technology, Iran.
    Saadati, Reza
    Iran University of Science and Technology, Iran.
    Ntouyas, Sotiris K.
    University of Ioannina, Greece;King Abdulaziz University, Saudi Arabia.
    Application of Fixed-Point Theory for a Nonlinear Fractional Three-Point Boundary-Value Problem2019In: Mathematics, E-ISSN 2227-7390, Vol. 7, no 6, p. 1-11, article id 526Article in journal (Refereed)
    Abstract [en]

    Throughout this paper, via the Schauder fixed-point theorem, a generalization of Krasnoselskii’s fixed-point theorem in a cone, as well as some inequalities relevant to Green’s function, we study the existence of positive solutions of a nonlinear, fractional three-point boundary-value problem with a term of the first order derivative [...]

  • 4.
    Saadati, R.
    et al.
    Iran Univ Sci & Technol, Iran.
    Pourhadi, Ehsan
    Linnaeus University, Faculty of Technology, Department of Mathematics. Iran Univ Sci & Technol, Iran.
    Samet, B.
    King Saud Univ, Saudi Arabia.
    On the PC-mild solutions of abstract fractional evolution equations with non-instantaneous impulses via the measure of noncompactness2019In: Boundary Value Problems, ISSN 1687-2762, E-ISSN 1687-2770, p. 1-23, article id 19Article in journal (Refereed)
    Abstract [en]

    In this paper, we deal with the existence results for mild solutions of abstract fractional evolution equations with non-instantaneous impulses on an unbounded interval. We also establish the existence of S-asymptotically -periodic mild solutions. The applied techniques are supported by the concept of measure of noncompactness in conjunction with the well-known Darbo-Sadovskii and Tichonov fixed-point theorems. Furthermore, an example to the fractional initial/boundary value Cauchy problem is concerned to illustrate our main results.

  • 5.
    Saadati, Reza
    et al.
    Iran University of Science and Technology, Iran.
    Pourhadi, Ehsan
    Linnaeus University, Faculty of Technology, Department of Mathematics. Iran University of Science and Technology, Iran.
    Mursaleen, Mohamad
    Aligarh Muslim University, India.
    Solvability of infinite systems of third-order differential equations in c0 by Meir-Keeler condensing operators2019In: Journal of Fixed Point Theory and Applications, ISSN 1661-7738, E-ISSN 1661-7746, Vol. 21, no 2, p. 1-16, article id 64Article in journal (Refereed)
    Abstract [en]

    Throughout this work, using the technique of measure of noncompactness together with Meir–Keeler condensing operators, we study the solvability of the following infinite system of third-order differential equations in the Banach sequence space c0 as a closed subspace of ℓ∞ :u′′′i+au′′i+bu′i+cui=fi(t,u1(t),u2(t),...)where fi∈C(R×R,R) is ω -periodic with respect to the first coordinate and a,b,c∈R are constant. Our approach depends on the Green's function corresponding to the aforesaid system and deduce some conclusions relevant to the existence of ω -periodic solutions in Banach sequence space c0 . In addition, some examples are supplied to illustrate the usefulness of the outcome.

    The full text will be freely available from 2020-05-04 09:06
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